LMFDB - Embedded newform 87.2.g.b.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (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:	$0.694698497585$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.3
Root			$2.41546 - 1.16323i$ of defining polynomial
Character	$\chi$	$=$	87.7
Dual form			87.2.g.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.596570 + 2.61374i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-4.67383 + 2.25080i) q^{4} +(-0.692177 - 3.03263i) q^{5} +(-0.596570 + 2.61374i) q^{6} +(2.13550 + 1.02840i) q^{7} +(-5.32817 - 6.68131i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(0.596570 + 2.61374i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-4.67383 + 2.25080i) q^{4} +(-0.692177 - 3.03263i) q^{5} +(-0.596570 + 2.61374i) q^{6} +(2.13550 + 1.02840i) q^{7} +(-5.32817 - 6.68131i) q^{8} +(0.623490 + 0.781831i) q^{9} +(7.51358 - 3.61835i) q^{10} +(1.62277 - 2.03489i) q^{11} -5.18756 q^{12} +(-1.43935 + 1.80488i) q^{13} +(-1.41401 + 6.19518i) q^{14} +(0.692177 - 3.03263i) q^{15} +(7.81583 - 9.80074i) q^{16} -4.83107 q^{17} +(-1.67155 + 2.09606i) q^{18} +(-1.47595 + 0.710781i) q^{19} +(10.0609 + 12.6160i) q^{20} +(1.47782 + 1.85312i) q^{21} +(6.28677 + 3.02755i) q^{22} +(0.263303 - 1.15361i) q^{23} +(-1.90160 - 8.33146i) q^{24} +(-4.21288 + 2.02881i) q^{25} +(-5.57617 - 2.68534i) q^{26} +(0.222521 + 0.974928i) q^{27} -12.2957 q^{28} +(5.05191 - 1.86501i) q^{29} +8.33945 q^{30} +(-1.28688 - 5.63821i) q^{31} +(14.8805 + 7.16606i) q^{32} +(2.34497 - 1.12928i) q^{33} +(-2.88207 - 12.6272i) q^{34} +(1.64062 - 7.18803i) q^{35} +(-4.67383 - 2.25080i) q^{36} +(4.30094 + 5.39321i) q^{37} +(-2.73831 - 3.43373i) q^{38} +(-2.07992 + 1.00163i) q^{39} +(-16.5739 + 20.7830i) q^{40} -7.66791 q^{41} +(-3.96197 + 4.96815i) q^{42} +(-0.419989 + 1.84009i) q^{43} +(-3.00442 + 13.1632i) q^{44} +(1.93944 - 2.43198i) q^{45} +3.17231 q^{46} +(-5.79950 + 7.27234i) q^{47} +(11.2942 - 5.43900i) q^{48} +(-0.861665 - 1.08049i) q^{49} +(-7.81608 - 9.80105i) q^{50} +(-4.35265 - 2.09612i) q^{51} +(2.66483 - 11.6754i) q^{52} +(1.15113 + 5.04343i) q^{53} +(-2.41546 + 1.16323i) q^{54} +(-7.29430 - 3.51275i) q^{55} +(-4.50723 - 19.7475i) q^{56} -1.63818 q^{57} +(7.88847 + 12.0918i) q^{58} -4.90494 q^{59} +(3.59071 + 15.7319i) q^{60} +(10.3934 + 5.00522i) q^{61} +(13.9691 - 6.72717i) q^{62} +(0.527426 + 2.31080i) q^{63} +(-4.27413 + 18.7262i) q^{64} +(6.46982 + 3.11570i) q^{65} +(4.35058 + 5.45546i) q^{66} +(-4.34830 - 5.45260i) q^{67} +(22.5796 - 10.8738i) q^{68} +(0.737759 - 0.925121i) q^{69} +19.7664 q^{70} +(2.32918 - 2.92070i) q^{71} +(1.90160 - 8.33146i) q^{72} +(-0.532592 + 2.33344i) q^{73} +(-11.5306 + 14.4590i) q^{74} -4.67594 q^{75} +(5.29852 - 6.64413i) q^{76} +(5.55812 - 2.67665i) q^{77} +(-3.85883 - 4.83882i) q^{78} +(2.34395 + 2.93923i) q^{79} +(-35.1319 - 16.9187i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-4.57445 - 20.0420i) q^{82} +(9.54570 - 4.59697i) q^{83} +(-11.0780 - 5.33491i) q^{84} +(3.34396 + 14.6508i) q^{85} -5.06009 q^{86} +(5.36081 + 0.511626i) q^{87} -22.2421 q^{88} +(1.26895 + 5.55963i) q^{89} +(7.51358 + 3.61835i) q^{90} +(-4.92988 + 2.37411i) q^{91} +(1.36590 + 5.98440i) q^{92} +(1.28688 - 5.63821i) q^{93} +(-22.4678 - 10.8199i) q^{94} +(3.17715 + 3.98402i) q^{95} +(10.2976 + 12.9128i) q^{96} +(-15.1300 + 7.28624i) q^{97} +(2.31009 - 2.89676i) q^{98} +2.60272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.596570	+	2.61374i	0.421839	+	1.84820i	0.521607	+	0.853186i	$0.325333\pi$
$2$	0.596570	+	2.61374i	0.421839	+	1.84820i	−0.0997685	+	0.995011i	$0.531810\pi$
$3$	0.900969	+	0.433884i	0.520175	+	0.250503i
$3$	0.900969	+	0.433884i	0.520175	+	0.250503i
$4$	−4.67383	+	2.25080i	−2.33691	+	1.12540i
$5$	−0.692177	−	3.03263i	−0.309551	−	1.35623i	−0.855235	−	0.518241i	$-0.826587\pi$
$5$	−0.692177	−	3.03263i	−0.309551	−	1.35623i	0.545684	−	0.837991i	$-0.316270\pi$
$6$	−0.596570	+	2.61374i	−0.243549	+	1.06706i
$7$	2.13550	+	1.02840i	0.807145	+	0.388701i	0.791494	−	0.611177i	$-0.209304\pi$
$7$	2.13550	+	1.02840i	0.807145	+	0.388701i	0.0156510	+	0.999878i	$0.495018\pi$
$8$	−5.32817	−	6.68131i	−1.88379	−	2.36220i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	7.51358	−	3.61835i	2.37600	−	1.14422i
$11$	1.62277	−	2.03489i	0.489283	−	0.613542i	−0.474491	−	0.880260i	$-0.657368\pi$
$11$	1.62277	−	2.03489i	0.489283	−	0.613542i	0.963774	+	0.266719i	$0.0859394\pi$
$12$	−5.18756			−1.49752
$13$	−1.43935	+	1.80488i	−0.399203	+	0.500584i	−0.940286	−	0.340384i	$-0.889443\pi$
$13$	−1.43935	+	1.80488i	−0.399203	+	0.500584i	0.541084	+	0.840969i	$0.318014\pi$
$14$	−1.41401	+	6.19518i	−0.377910	+	1.65573i
$15$	0.692177	−	3.03263i	0.178719	−	0.783021i
$16$	7.81583	−	9.80074i	1.95396	−	2.45019i
$17$	−4.83107			−1.17171			−0.585854	−	0.810417i	$-0.699241\pi$
$17$	−4.83107			−1.17171			−0.585854	+	0.810417i	$0.699241\pi$
$18$	−1.67155	+	2.09606i	−0.393989	+	0.494046i
$19$	−1.47595	+	0.710781i	−0.338606	+	0.163064i	−0.595458	−	0.803387i	$-0.703029\pi$
$19$	−1.47595	+	0.710781i	−0.338606	+	0.163064i	0.256851	+	0.966451i	$0.417315\pi$
$20$	10.0609	+	12.6160i	2.24970	+	2.82103i
$21$	1.47782	+	1.85312i	0.322486	+	0.404384i
$22$	6.28677	+	3.02755i	1.34034	+	0.645476i
$23$	0.263303	−	1.15361i	0.0549025	−	0.240544i	−0.940030	−	0.341093i	$-0.889203\pi$
$23$	0.263303	−	1.15361i	0.0549025	−	0.240544i	0.994932	+	0.100549i	$0.0320600\pi$
$24$	−1.90160	−	8.33146i	−0.388163	−	1.70065i
$25$	−4.21288	+	2.02881i	−0.842575	+	0.405763i
$26$	−5.57617	−	2.68534i	−1.09358	−	0.526639i
$27$	0.222521	+	0.974928i	0.0428242	+	0.187625i
$28$	−12.2957			−2.32367
$29$	5.05191	−	1.86501i	0.938115	−	0.346323i
$29$	5.05191	−	1.86501i	0.938115	−	0.346323i
$30$	8.33945			1.52257
$31$	−1.28688	−	5.63821i	−0.231131	−	1.01265i	−0.948703	−	0.316168i	$-0.897604\pi$
$31$	−1.28688	−	5.63821i	−0.231131	−	1.01265i	0.717572	−	0.696484i	$-0.245253\pi$
$32$	14.8805	+	7.16606i	2.63052	+	1.26679i
$33$	2.34497	−	1.12928i	0.408207	−	0.196582i
$34$	−2.88207	−	12.6272i	−0.494272	−	2.16555i
$35$	1.64062	−	7.18803i	0.277316	−	1.21500i
$36$	−4.67383	−	2.25080i	−0.778971	−	0.375133i
$37$	4.30094	+	5.39321i	0.707070	+	0.886637i	0.997529	−	0.0702498i	$-0.0223796\pi$
$37$	4.30094	+	5.39321i	0.707070	+	0.886637i	−0.290460	+	0.956887i	$0.593808\pi$
$38$	−2.73831	−	3.43373i	−0.444212	−	0.557024i
$39$	−2.07992	+	1.00163i	−0.333053	+	0.160390i
$40$	−16.5739	+	20.7830i	−2.62056	+	3.28608i
$41$	−7.66791			−1.19753			−0.598763	−	0.800926i	$-0.704341\pi$
$41$	−7.66791			−1.19753			−0.598763	+	0.800926i	$0.704341\pi$
$42$	−3.96197	+	4.96815i	−0.611345	+	0.766602i
$43$	−0.419989	+	1.84009i	−0.0640478	+	0.280612i	−0.996803	−	0.0798987i	$-0.974540\pi$
$43$	−0.419989	+	1.84009i	−0.0640478	+	0.280612i	0.932755	+	0.360510i	$0.117397\pi$
$44$	−3.00442	+	13.1632i	−0.452934	+	1.98443i
$45$	1.93944	−	2.43198i	0.289114	−	0.362538i
$46$	3.17231			0.467732
$47$	−5.79950	+	7.27234i	−0.845944	+	1.06078i	0.151438	+	0.988467i	$0.451610\pi$
$47$	−5.79950	+	7.27234i	−0.845944	+	1.06078i	−0.997382	+	0.0723132i	$0.976962\pi$
$48$	11.2942	−	5.43900i	1.63018	−	0.785052i
$49$	−0.861665	−	1.08049i	−0.123095	−	0.154356i
$50$	−7.81608	−	9.80105i	−1.10536	−	1.38608i
$51$	−4.35265	−	2.09612i	−0.609493	−	0.293516i
$52$	2.66483	−	11.6754i	0.369545	−	1.61908i
$53$	1.15113	+	5.04343i	0.158120	+	0.692768i	0.990379	+	0.138381i	$0.0441899\pi$
$53$	1.15113	+	5.04343i	0.158120	+	0.692768i	−0.832259	+	0.554387i	$0.812953\pi$
$54$	−2.41546	+	1.16323i	−0.328703	+	0.158295i
$55$	−7.29430	−	3.51275i	−0.983563	−	0.473659i
$56$	−4.50723	−	19.7475i	−0.602304	−	2.63887i
$57$	−1.63818			−0.216983
$58$	7.88847	+	12.0918i	1.03581	+	1.58773i
$59$	−4.90494			−0.638569			−0.319285	−	0.947659i	$-0.603443\pi$
$59$	−4.90494			−0.638569			−0.319285	+	0.947659i	$0.603443\pi$
$60$	3.59071	+	15.7319i	0.463559	+	2.03098i
$61$	10.3934	+	5.00522i	1.33074	+	0.640852i	0.957916	−	0.287048i	$-0.0926740\pi$
$61$	10.3934	+	5.00522i	1.33074	+	0.640852i	0.372828	+	0.927901i	$0.378388\pi$
$62$	13.9691	−	6.72717i	1.77408	−	0.854352i
$63$	0.527426	+	2.31080i	0.0664494	+	0.291134i
$64$	−4.27413	+	18.7262i	−0.534266	+	2.34077i
$65$	6.46982	+	3.11570i	0.802482	+	0.386455i
$66$	4.35058	+	5.45546i	0.535519	+	0.671520i
$67$	−4.34830	−	5.45260i	−0.531229	−	0.666141i	0.441722	−	0.897152i	$-0.354368\pi$
$67$	−4.34830	−	5.45260i	−0.531229	−	0.666141i	−0.972951	+	0.231012i	$0.925796\pi$
$68$	22.5796	−	10.8738i	2.73818	−	1.31864i
$69$	0.737759	−	0.925121i	0.0888158	−	0.111371i
$70$	19.7664			2.36254
$71$	2.32918	−	2.92070i	0.276423	−	0.346623i	−0.624169	−	0.781289i	$-0.714562\pi$
$71$	2.32918	−	2.92070i	0.276423	−	0.346623i	0.900592	+	0.434666i	$0.143134\pi$
$72$	1.90160	−	8.33146i	0.224106	−	0.981871i
$73$	−0.532592	+	2.33344i	−0.0623351	+	0.273108i	−0.996485	−	0.0837733i	$-0.973303\pi$
$73$	−0.532592	+	2.33344i	−0.0623351	+	0.273108i	0.934150	+	0.356881i	$0.116160\pi$
$74$	−11.5306	+	14.4590i	−1.34041	+	1.68082i
$75$	−4.67594			−0.539931
$76$	5.29852	−	6.64413i	0.607782	−	0.762134i
$77$	5.55812	−	2.67665i	0.633406	−	0.305032i
$78$	−3.85883	−	4.83882i	−0.436927	−	0.547889i
$79$	2.34395	+	2.93923i	0.263716	+	0.330689i	0.896005	−	0.444043i	$-0.146456\pi$
$79$	2.34395	+	2.93923i	0.263716	+	0.330689i	−0.632290	+	0.774732i	$0.717885\pi$
$80$	−35.1319	−	16.9187i	−3.92787	−	1.89156i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	−4.57445	−	20.0420i	−0.505163	−	2.21326i
$83$	9.54570	−	4.59697i	1.04778	−	0.504583i	0.170895	−	0.985289i	$-0.445334\pi$
$83$	9.54570	−	4.59697i	1.04778	−	0.504583i	0.876882	+	0.480707i	$0.159620\pi$
$84$	−11.0780	−	5.33491i	−1.20871	−	0.582086i
$85$	3.34396	+	14.6508i	0.362703	+	1.58911i
$86$	−5.06009			−0.545643
$87$	5.36081	+	0.511626i	0.574739	+	0.0548521i
$88$	−22.2421			−2.37101
$89$	1.26895	+	5.55963i	0.134508	+	0.589320i	0.996587	+	0.0825457i	$0.0263050\pi$
$89$	1.26895	+	5.55963i	0.134508	+	0.589320i	−0.862079	+	0.506774i	$0.830838\pi$
$90$	7.51358	+	3.61835i	0.792001	+	0.381408i
$91$	−4.92988	+	2.37411i	−0.516792	+	0.248874i
$92$	1.36590	+	5.98440i	0.142405	+	0.623917i
$93$	1.28688	−	5.63821i	0.133444	−	0.584655i
$94$	−22.4678	−	10.8199i	−2.31738	−	1.11599i
$95$	3.17715	+	3.98402i	0.325969	+	0.408752i
$96$	10.2976	+	12.9128i	1.05100	+	1.31791i
$97$	−15.1300	+	7.28624i	−1.53622	+	0.739806i	−0.994886	−	0.101000i	$-0.967796\pi$
$97$	−15.1300	+	7.28624i	−1.53622	+	0.739806i	−0.541337	+	0.840806i	$0.682082\pi$
$98$	2.31009	−	2.89676i	0.233354	−	0.292617i
$99$	2.60272			0.261583
$100$	15.1238	−	18.9646i	1.51238	−	1.89646i
$101$	−1.01964	+	4.46734i	−0.101458	+	0.444517i	0.898526	+	0.438920i	$0.144639\pi$
$101$	−1.01964	+	4.46734i	−0.101458	+	0.444517i	−0.999984	+	0.00559720i	$0.998218\pi$
$102$	2.88207	−	12.6272i	0.285368	−	1.25028i
$103$	6.56608	−	8.23361i	0.646975	−	0.811281i	−0.344881	−	0.938647i	$-0.612081\pi$
$103$	6.56608	−	8.23361i	0.646975	−	0.811281i	0.991856	+	0.127365i	$0.0406521\pi$
$104$	19.7281			1.93449
$105$	4.59692	−	5.76435i	0.448613	−	0.562543i
$106$	−12.4955	+	6.01751i	−1.21367	+	0.584473i
$107$	8.57509	+	10.7528i	0.828985	+	1.03951i	0.998541	+	0.0539937i	$0.0171951\pi$
$107$	8.57509	+	10.7528i	0.828985	+	1.03951i	−0.169556	+	0.985520i	$0.554233\pi$
$108$	−3.23439	−	4.05579i	−0.311229	−	0.390269i
$109$	4.82225	+	2.32227i	0.461888	+	0.222434i	0.650332	−	0.759650i	$-0.274630\pi$
$109$	4.82225	+	2.32227i	0.461888	+	0.222434i	−0.188444	+	0.982084i	$0.560344\pi$
$110$	4.82987	−	21.1610i	0.460510	−	2.01763i
$111$	1.53499	+	6.72522i	0.145695	+	0.638329i
$112$	26.7699	−	12.8917i	2.52952	−	1.21815i
$113$	9.72860	+	4.68504i	0.915189	+	0.440732i	0.831351	−	0.555747i	$-0.187568\pi$
$113$	9.72860	+	4.68504i	0.915189	+	0.440732i	0.0838381	+	0.996479i	$0.473282\pi$
$114$	−0.977290	−	4.28179i	−0.0915316	−	0.401026i
$115$	−3.68071			−0.343228
$116$	−19.4140	+	20.0875i	−1.80254	+	1.86508i
$117$	−2.30853			−0.213424
$118$	−2.92614	−	12.8203i	−0.269373	−	1.18020i
$119$	−10.3168	−	4.96830i	−0.945738	−	0.455443i
$120$	−23.9500	+	11.5337i	−2.18632	+	1.05288i
$121$	0.940341	+	4.11990i	0.0854856	+	0.374537i
$122$	−6.88194	+	30.1518i	−0.623062	+	2.72981i
$123$	−6.90855	−	3.32698i	−0.622923	−	0.299984i
$124$	18.7051	+	23.4555i	1.67977	+	2.10637i
$125$	−0.628496	−	0.788109i	−0.0562144	−	0.0704906i
$126$	−5.72521	+	2.75711i	−0.510042	+	0.245623i
$127$	10.5127	−	13.1825i	0.932851	−	1.16976i	−0.0523973	−	0.998626i	$-0.516686\pi$
$127$	10.5127	−	13.1825i	0.932851	−	1.16976i	0.985248	−	0.171132i	$-0.0547423\pi$
$128$	−18.4631			−1.63192
$129$	−1.17678	+	1.47564i	−0.103610	+	0.129923i
$130$	−4.28394	+	18.7692i	−0.375727	+	1.64617i
$131$	−1.01316	+	4.43896i	−0.0885206	+	0.387834i	−0.999708	−	0.0241577i	$-0.992310\pi$
$131$	−1.01316	+	4.43896i	−0.0885206	+	0.387834i	0.911188	+	0.411992i	$0.135167\pi$
$132$	−8.41820	+	10.5561i	−0.732710	+	0.918790i
$133$	−3.88287			−0.336688
$134$	11.6576	−	14.6182i	1.00707	−	1.26282i
$135$	2.80257	−	1.34965i	0.241207	−	0.116159i
$136$	25.7408	+	32.2779i	2.20725	+	2.76781i
$137$	−13.7225	−	17.2075i	−1.17239	−	1.47014i	−0.852534	−	0.522672i	$-0.824935\pi$
$137$	−13.7225	−	17.2075i	−1.17239	−	1.47014i	−0.319861	−	0.947465i	$-0.603636\pi$
$138$	2.85816	+	1.37642i	0.243302	+	0.117168i
$139$	1.80101	−	7.89075i	0.152760	−	0.669284i	−0.839316	−	0.543644i	$-0.817044\pi$
$139$	1.80101	−	7.89075i	0.152760	−	0.669284i	0.992076	−	0.125641i	$-0.0400986\pi$
$140$	8.51081	+	37.2883i	0.719295	+	3.15144i
$141$	−8.38052	+	4.03584i	−0.705767	+	0.339879i
$142$	9.02347	+	4.34548i	0.757233	+	0.364664i
$143$	1.33701	+	5.85781i	0.111806	+	0.489855i
$144$	12.5356			1.04464
$145$	−9.15269	−	14.0296i	−0.760089	−	1.16510i
$146$	−6.41673			−0.531053
$147$	−0.307525	−	1.34735i	−0.0253642	−	0.111128i
$148$	−32.2408	−	15.5264i	−2.65018	−	1.27626i
$149$	−0.670037	+	0.322673i	−0.0548916	+	0.0264344i	−0.461128	−	0.887334i	$-0.652555\pi$
$149$	−0.670037	+	0.322673i	−0.0548916	+	0.0264344i	0.406237	+	0.913768i	$0.366841\pi$
$150$	−2.78953	−	12.2217i	−0.227764	−	0.997898i
$151$	3.84695	−	16.8546i	0.313060	−	1.37161i	−0.536404	−	0.843961i	$-0.680218\pi$
$151$	3.84695	−	16.8546i	0.313060	−	1.37161i	0.849465	−	0.527646i	$-0.176925\pi$
$152$	12.6131	+	6.07413i	1.02305	+	0.492677i
$153$	−3.01213	−	3.77709i	−0.243516	−	0.305359i
$154$	10.3119	+	12.9307i	0.830955	+	1.04198i
$155$	−16.2078	+	7.80528i	−1.30184	+	0.626935i
$156$	7.46669	−	9.36293i	0.597813	−	0.749634i
$157$	−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
$159$	−1.15113	+	5.04343i	−0.0912905	+	0.399970i
$160$	11.4321	−	50.0872i	0.903784	−	3.95974i
$161$	1.74866	−	2.19275i	0.137814	−	0.172813i
$162$	−2.68096			−0.210636
$163$	6.18092	−	7.75063i	0.484127	−	0.607076i	−0.478440	−	0.878120i	$-0.658798\pi$
$163$	6.18092	−	7.75063i	0.484127	−	0.607076i	0.962567	+	0.271044i	$0.0873690\pi$
$164$	35.8385	−	17.2589i	2.79852	−	1.34769i
$165$	−5.04781	−	6.32976i	−0.392972	−	0.492771i
$166$	17.7100	+	22.2076i	1.37456	+	1.72364i
$167$	10.5584	+	5.08467i	0.817036	+	0.393464i	0.795237	−	0.606298i	$-0.207346\pi$
$167$	10.5584	+	5.08467i	0.817036	+	0.393464i	0.0217990	+	0.999762i	$0.493061\pi$
$168$	4.50723	−	19.7475i	0.347741	−	1.52355i
$169$	1.70689	+	7.47836i	0.131299	+	0.575259i
$170$	−36.2987	+	17.4805i	−2.78398	+	1.34069i
$171$	−1.47595	−	0.710781i	−0.112869	−	0.0543547i
$172$	−2.17872	−	9.54559i	−0.166126	−	0.727844i
$173$	8.14339			0.619131			0.309565	−	0.950878i	$-0.399816\pi$
$173$	8.14339			0.619131			0.309565	+	0.950878i	$0.399816\pi$
$174$	1.86084	+	14.3170i	0.141070	+	1.08537i
$175$	−11.0831			−0.837800
$176$	−7.26012	−	31.8087i	−0.547252	−	2.39767i
$177$	−4.41920	−	2.12818i	−0.332168	−	0.159963i
$178$	−13.7744	+	6.63342i	−1.03244	+	0.497196i
$179$	−2.39845	−	10.5083i	−0.179268	−	0.785426i	−0.981969	−	0.189044i	$-0.939461\pi$
$179$	−2.39845	−	10.5083i	−0.179268	−	0.785426i	0.802700	−	0.596383i	$-0.203396\pi$
$180$	−3.59071	+	15.7319i	−0.267636	+	1.17259i
$181$	−18.5712	−	8.94342i	−1.38039	−	0.664759i	−0.411305	−	0.911498i	$-0.634927\pi$
$181$	−18.5712	−	8.94342i	−1.38039	−	0.664759i	−0.969082	+	0.246738i	$0.920641\pi$
$182$	−9.14632	−	11.4691i	−0.677971	−	0.850148i
$183$	7.19248	+	9.01909i	0.531684	+	0.666710i
$184$	−9.11053	+	4.38740i	−0.671637	+	0.323443i
$185$	13.3786	−	16.7762i	0.983612	−	1.23341i
$186$	15.5046			1.13685
$187$	−7.83972	+	9.83069i	−0.573297	+	0.718891i
$188$	10.7373	−	47.0431i	0.783097	−	3.43097i
$189$	−0.527426	+	2.31080i	−0.0383646	+	0.168086i
$190$	−8.51782	+	10.6810i	−0.617948	+	0.774882i
$191$	−24.4869			−1.77181			−0.885906	−	0.463865i	$-0.846462\pi$
$191$	−24.4869			−1.77181			−0.885906	+	0.463865i	$0.846462\pi$
$192$	−11.9758	+	15.0172i	−0.864282	+	1.08378i
$193$	14.2742	−	6.87409i	1.02748	−	0.494808i	0.157303	−	0.987550i	$-0.449720\pi$
$193$	14.2742	−	6.87409i	1.02748	−	0.494808i	0.870175	+	0.492743i	$0.164006\pi$
$194$	−28.0705	−	35.1993i	−2.01535	−	2.52716i
$195$	4.47725	+	5.61430i	0.320623	+	0.402048i
$196$	6.45924	+	3.11061i	0.461374	+	0.222186i
$197$	−2.83725	+	12.4308i	−0.202146	+	0.885660i	0.767481	+	0.641072i	$0.221510\pi$
$197$	−2.83725	+	12.4308i	−0.202146	+	0.885660i	−0.969627	+	0.244588i	$0.921347\pi$
$198$	1.55270	+	6.80284i	0.110346	+	0.483457i
$199$	7.32020	−	3.52522i	0.518915	−	0.249896i	−0.156046	−	0.987750i	$-0.549875\pi$
$199$	7.32020	−	3.52522i	0.518915	−	0.249896i	0.674961	+	0.737853i	$0.264160\pi$
$200$	36.0020	+	17.3377i	2.54573	+	1.22596i
$201$	−1.55189	−	6.79927i	−0.109462	−	0.479584i
$202$	−12.2848			−0.864354
$203$	12.7064	+	1.21267i	0.891811	+	0.0851129i
$204$	25.0615			1.75465
$205$	5.30756	+	23.2539i	0.370696	+	1.62412i
$206$	25.4377	+	12.2501i	1.77233	+	0.853507i
$207$	1.06609	−	0.513403i	0.0740986	−	0.0356840i
$208$	6.43951	+	28.2133i	0.446499	+	1.95624i
$209$	−0.948769	+	4.15683i	−0.0656277	+	0.287534i
$210$	17.8089	+	8.57633i	1.22893	+	0.591823i
$211$	−13.0904	−	16.4149i	−0.901183	−	1.13005i	−0.990970	−	0.134086i	$-0.957190\pi$
$211$	−13.0904	−	16.4149i	−0.901183	−	1.13005i	0.0897871	−	0.995961i	$-0.471381\pi$
$212$	−16.7319	−	20.9811i	−1.14915	−	1.44099i
$213$	3.36576	−	1.62086i	0.230618	−	0.111060i
$214$	−22.9895	+	28.8279i	−1.57153	+	1.97063i
$215$	5.87102			0.400401
$216$	5.32817	−	6.68131i	0.362536	−	0.454605i
$217$	3.05021	−	13.3639i	0.207062	−	0.907198i
$218$	−3.19302	+	13.9895i	−0.216259	+	0.947491i
$219$	−1.49229	+	1.87127i	−0.100840	+	0.126449i
$220$	41.9988			2.83156
$221$	6.95359	−	8.71952i	0.467749	−	0.586538i
$222$	−16.6623	+	8.02413i	−1.11830	+	0.538544i
$223$	13.2224	+	16.5803i	0.885436	+	1.11030i	0.993234	+	0.116128i	$0.0370484\pi$
$223$	13.2224	+	16.5803i	0.885436	+	1.11030i	−0.107799	+	0.994173i	$0.534380\pi$
$224$	24.4077	+	30.6063i	1.63081	+	2.04497i
$225$	−4.21288	−	2.02881i	−0.280858	−	0.135254i
$226$	−6.44172	+	28.2230i	−0.428497	+	1.87737i
$227$	−2.38193	−	10.4359i	−0.158094	−	0.692656i	−0.990388	−	0.138320i	$-0.955830\pi$
$227$	−2.38193	−	10.4359i	−0.158094	−	0.692656i	0.832293	−	0.554335i	$-0.187028\pi$
$228$	7.65658	−	3.68721i	0.507069	−	0.244192i
$229$	12.6188	+	6.07690i	0.833875	+	0.401573i	0.801567	−	0.597905i	$-0.204000\pi$
$229$	12.6188	+	6.07690i	0.833875	+	0.401573i	0.0323077	+	0.999478i	$0.489714\pi$
$230$	−2.19580	−	9.62044i	−0.144787	−	0.634353i
$231$	6.16905			0.405893
$232$	−39.3781	−	23.8163i	−2.58530	−	1.56361i
$233$	−12.3851			−0.811377			−0.405688	−	0.914011i	$-0.632968\pi$
$233$	−12.3851			−0.811377			−0.405688	+	0.914011i	$0.632968\pi$
$234$	−1.37720	−	6.03391i	−0.0900304	−	0.394449i
$235$	26.0686	+	12.5540i	1.70053	+	0.818931i
$236$	22.9249	−	11.0400i	1.49228	−	0.718645i
$237$	0.836548	+	3.66516i	0.0543396	+	0.238077i
$238$	6.83118	−	29.9294i	0.442800	−	1.94003i
$239$	−8.02168	−	3.86304i	−0.518879	−	0.249879i	0.156066	−	0.987747i	$-0.450119\pi$
$239$	−8.02168	−	3.86304i	−0.518879	−	0.249879i	−0.674946	+	0.737867i	$0.735833\pi$
$240$	−24.3121	−	30.4864i	−1.56934	−	1.96789i
$241$	−16.3041	−	20.4447i	−1.05024	−	1.31696i	−0.946623	−	0.322344i	$-0.895529\pi$
$241$	−16.3041	−	20.4447i	−1.05024	−	1.31696i	−0.103619	−	0.994617i	$-0.533042\pi$
$242$	−10.2074	+	4.91562i	−0.656156	+	0.315988i
$243$	−0.623490	+	0.781831i	−0.0399969	+	0.0501545i
$244$	−59.8429			−3.83105
$245$	−2.68031	+	3.36100i	−0.171239	+	0.214726i
$246$	4.57445	−	20.0420i	0.291656	−	1.27783i
$247$	0.841529	−	3.68698i	0.0535452	−	0.234597i
$248$	−30.8139	+	38.6394i	−1.95668	+	2.45360i
$249$	10.5949			0.671426
$250$	1.68497	−	2.11289i	0.106567	−	0.133631i
$251$	−3.49262	+	1.68196i	−0.220452	+	0.106164i	−0.540851	−	0.841119i	$-0.681898\pi$
$251$	−3.49262	+	1.68196i	−0.220452	+	0.106164i	0.320398	+	0.947283i	$0.396183\pi$
$252$	−7.66625	−	9.61317i	−0.482928	−	0.605573i
$253$	−1.92018	−	2.40783i	−0.120721	−	0.151379i
$254$	40.7273	+	19.6132i	2.55546	+	1.23064i
$255$	−3.34396	+	14.6508i	−0.209407	+	0.917472i
$256$	−2.46628	−	10.8055i	−0.154142	−	0.675341i
$257$	1.45625	−	0.701292i	0.0908383	−	0.0437454i	−0.387913	−	0.921696i	$-0.626804\pi$
$257$	1.45625	−	0.701292i	0.0908383	−	0.0437454i	0.478751	+	0.877951i	$0.341090\pi$
$258$	−4.55898	−	2.19549i	−0.283830	−	0.136685i
$259$	3.63827	+	15.9403i	0.226071	+	0.990483i
$260$	−37.2516			−2.31025
$261$	4.60793	+	2.78693i	0.285224	+	0.172506i
$262$	−12.2067			−0.754135
$263$	5.04283	+	22.0941i	0.310954	+	1.36238i	0.852948	+	0.521996i	$0.174812\pi$
$263$	5.04283	+	22.0941i	0.310954	+	1.36238i	−0.541994	+	0.840382i	$0.682331\pi$
$264$	−20.0394	−	9.65048i	−1.23334	−	0.593946i
$265$	14.4980	−	6.98189i	0.890608	−	0.428894i
$266$	−2.31640	−	10.1488i	−0.142028	−	0.622265i
$267$	−1.26895	+	5.55963i	−0.0776585	+	0.340244i
$268$	32.5959	+	15.6973i	1.99111	+	0.958868i
$269$	−3.25476	−	4.08133i	−0.198446	−	0.248843i	0.672645	−	0.739966i	$-0.265158\pi$
$269$	−3.25476	−	4.08133i	−0.198446	−	0.248843i	−0.871091	+	0.491122i	$0.836587\pi$
$270$	5.19956	+	6.52004i	0.316435	+	0.396797i
$271$	−1.35089	+	0.650556i	−0.0820610	+	0.0395185i	−0.474464	−	0.880275i	$-0.657358\pi$
$271$	−1.35089	+	0.650556i	−0.0820610	+	0.0395185i	0.392403	+	0.919793i	$0.371644\pi$
$272$	−37.7589	+	47.3481i	−2.28947	+	2.87090i
$273$	−5.47175			−0.331166
$274$	36.7896	−	46.1327i	2.22254	−	2.78698i
$275$	−2.70811	+	11.8650i	−0.163305	+	0.715488i
$276$	−1.36590	+	5.98440i	−0.0822175	+	0.360219i
$277$	1.35995	−	1.70532i	0.0817112	−	0.102463i	−0.739296	−	0.673381i	$-0.764841\pi$
$277$	1.35995	−	1.70532i	0.0817112	−	0.102463i	0.821007	+	0.570918i	$0.193413\pi$
$278$	21.6988			1.30141
$279$	3.60577	−	4.52149i	0.215872	−	0.270695i
$280$	−56.7669	+	27.3375i	−3.39247	+	1.63373i
$281$	−10.7411	−	13.4689i	−0.640761	−	0.803489i	0.350337	−	0.936624i	$-0.386067\pi$
$281$	−10.7411	−	13.4689i	−0.640761	−	0.803489i	−0.991098	+	0.133135i	$0.957496\pi$
$282$	−15.5482	−	19.4969i	−0.925884	−	1.16102i
$283$	10.2985	+	4.95949i	0.612182	+	0.294811i	0.714168	−	0.699975i	$-0.246805\pi$
$283$	10.2985	+	4.95949i	0.612182	+	0.294811i	−0.101986	+	0.994786i	$0.532520\pi$
$284$	−4.31228	+	18.8933i	−0.255887	+	1.12111i
$285$	1.13391	+	4.96800i	0.0671672	+	0.294279i
$286$	−14.5132	+	6.98919i	−0.858184	+	0.413280i
$287$	−16.3749	−	7.88572i	−0.966578	−	0.465479i
$288$	3.67518	+	16.1020i	0.216562	+	0.948819i
$289$	6.33927			0.372898
$290$	31.2097	−	32.2924i	1.83269	−	1.89628i
$291$	−16.7931			−0.984428
$292$	−2.76285	−	12.1048i	−0.161683	−	0.708382i
$293$	4.61704	+	2.22345i	0.269730	+	0.129895i	0.563860	−	0.825870i	$-0.309316\pi$
$293$	4.61704	+	2.22345i	0.269730	+	0.129895i	−0.294130	+	0.955765i	$0.595030\pi$
$294$	3.33818	−	1.60758i	0.194686	−	0.0937560i
$295$	3.39509	+	14.8749i	0.197670	+	0.866048i
$296$	13.1176	−	57.4718i	0.762443	−	3.34048i
$297$	2.34497	+	1.12928i	0.136069	+	0.0655273i
$298$	−1.24311	−	1.55881i	−0.0720114	−	0.0902994i
$299$	1.70314	+	2.13567i	0.0984952	+	0.123509i
$300$	21.8545	−	10.5246i	1.26177	−	0.607637i
$301$	−2.78925	+	3.49761i	−0.160770	+	0.201599i
$302$	46.3486			2.66706
$303$	−2.85697	+	3.58253i	−0.164129	+	0.205811i
$304$	−4.56961	+	20.0208i	−0.262085	+	1.14827i
$305$	7.98485	−	34.9839i	0.457211	−	2.00317i
$306$	8.07539	−	10.1262i	0.461639	−	0.578878i
$307$	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
$309$	9.48826	−	4.56931i	0.539768	−	0.259939i
$310$	−30.0701	−	37.7067i	−1.70787	−	2.14160i
$311$	10.6731	+	13.3836i	0.605213	+	0.758913i	0.986180	−	0.165675i	$-0.0529803\pi$
$311$	10.6731	+	13.3836i	0.605213	+	0.758913i	−0.380967	+	0.924589i	$0.624409\pi$
$312$	17.7744	+	8.55968i	1.00628	+	0.484597i
$313$	0.322250	−	1.41187i	0.0182147	−	0.0798036i	−0.965004	−	0.262236i	$-0.915540\pi$
$313$	0.322250	−	1.41187i	0.0182147	−	0.0798036i	0.983218	+	0.182433i	$0.0583972\pi$
$314$	−0.238202	−	1.04363i	−0.0134425	−	0.0588955i
$315$	6.64274	−	3.19897i	0.374276	−	0.180242i
$316$	−17.5708	−	8.46167i	−0.988437	−	0.476006i
$317$	3.89788	+	17.0777i	0.218927	+	0.959182i	0.958273	+	0.285856i	$0.0922779\pi$
$317$	3.89788	+	17.0777i	0.218927	+	0.959182i	−0.739346	+	0.673326i	$0.764865\pi$
$318$	−13.8690			−0.777732
$319$	4.40299	−	13.3065i	0.246520	−	0.745023i
$320$	59.7480			3.34002
$321$	3.06041	+	13.4085i	0.170816	+	0.748392i
$322$	6.77449	+	3.26242i	0.377528	+	0.181808i
$323$	7.13043	−	3.43383i	0.396748	−	0.191064i
$324$	−1.15434	−	5.05749i	−0.0641300	−	0.280972i
$325$	2.40201	−	10.5239i	0.133240	−	0.583762i
$326$	23.9455	+	11.5316i	1.32622	+	0.638674i
$327$	3.33710	+	4.18459i	0.184542	+	0.231409i
$328$	40.8559	+	51.2317i	2.25589	+	2.82880i
$329$	−19.8638	+	9.56589i	−1.09512	+	0.527384i
$330$	13.5330	−	16.9698i	0.744967	−	0.934159i
$331$	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
$333$	−1.53499	+	6.72522i	−0.0841168	+	0.368540i
$334$	−6.99119	+	30.6304i	−0.382541	+	1.67602i
$335$	−13.5259	+	16.9609i	−0.738999	+	0.926675i
$336$	29.7123			1.62094
$337$	−20.0771	+	25.1759i	−1.09367	+	1.37142i	−0.171254	+	0.985227i	$0.554782\pi$
$337$	−20.0771	+	25.1759i	−1.09367	+	1.37142i	−0.922418	+	0.386194i	$0.873790\pi$
$338$	−18.5282	+	8.92273i	−1.00780	+	0.485333i
$339$	6.73240	+	8.44216i	0.365654	+	0.458515i
$340$	−48.6052	−	60.9489i	−2.63598	−	3.30542i
$341$	−13.5614	−	6.53084i	−0.734393	−	0.353665i
$342$	0.977290	−	4.28179i	0.0528458	−	0.231533i
$343$	−4.42089	−	19.3692i	−0.238705	−	1.04584i
$344$	14.5320	−	6.99824i	0.783513	−	0.377320i
$345$	−3.31621	−	1.59700i	−0.178539	−	0.0859797i
$346$	4.85811	+	21.2848i	0.261173	+	1.14428i
$347$	6.96578			0.373942			0.186971	−	0.982365i	$-0.440133\pi$
$347$	6.96578			0.373942			0.186971	+	0.982365i	$0.440133\pi$
$348$	−26.2070	+	9.67483i	−1.40484	+	0.518625i
$349$	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
$351$	−2.07992	−	1.00163i	−0.111018	−	0.0534633i
$352$	38.7297	−	18.6513i	2.06430	−	0.994115i
$353$	−5.75044	−	25.1943i	−0.306065	−	1.34096i	−0.860805	−	0.508935i	$-0.830039\pi$
$353$	−5.75044	−	25.1943i	−0.306065	−	1.34096i	0.554740	−	0.832024i	$-0.312818\pi$
$354$	2.92614	−	12.8203i	0.155523	−	0.681390i
$355$	−10.4696	−	5.04189i	−0.555668	−	0.267596i
$356$	−18.4444	−	23.1286i	−0.977554	−	1.22581i
$357$	−7.13943	−	8.95257i	−0.377859	−	0.473820i
$358$	26.0351	−	12.5379i	1.37600	−	0.662646i
$359$	−10.9382	+	13.7160i	−0.577295	+	0.723905i	−0.981649	−	0.190698i	$-0.938925\pi$
$359$	−10.9382	+	13.7160i	−0.577295	+	0.723905i	0.404354	+	0.914603i	$0.367496\pi$
$360$	−26.5824			−1.40102
$361$	−10.1731	+	12.7566i	−0.535425	+	0.671402i
$362$	12.2968	−	53.8758i	0.646305	−	2.83165i
$363$	−0.940341	+	4.11990i	−0.0493551	+	0.216239i
$364$	17.6978	−	22.1923i	0.927616	−	1.16319i
$365$	7.44509			0.389694
$366$	−19.2828	+	24.1798i	−1.00793	+	1.26390i
$367$	−26.8154	+	12.9136i	−1.39975	+	0.674086i	−0.973112	−	0.230334i	$-0.926018\pi$
$367$	−26.8154	+	12.9136i	−1.39975	+	0.674086i	−0.426643	+	0.904420i	$0.640304\pi$
$368$	−9.24827	−	11.5970i	−0.482100	−	0.604534i
$369$	−4.78087	−	5.99502i	−0.248882	−	0.312088i
$370$	51.8299	+	24.9600i	2.69451	+	1.29761i
$371$	−2.72844	+	11.9541i	−0.141654	+	0.620625i
$372$	6.67578	+	29.2485i	0.346123	+	1.51647i
$373$	−17.3846	+	8.37200i	−0.900142	+	0.433485i	−0.825940	−	0.563758i	$-0.809355\pi$
$373$	−17.3846	+	8.37200i	−0.900142	+	0.433485i	−0.0742017	+	0.997243i	$0.523641\pi$
$374$	−30.3719	−	14.6263i	−1.57049	−	0.756309i
$375$	−0.224308	−	0.982756i	−0.0115832	−	0.0507493i
$376$	79.4894			4.09936
$377$	−3.90532	+	11.8025i	−0.201134	+	0.607859i
$378$	−6.35450			−0.326840
$379$	1.91129	+	8.37391i	0.0981763	+	0.430139i	0.999998	−	0.00196965i	$-0.000626959\pi$
$379$	1.91129	+	8.37391i	0.0981763	+	0.430139i	−0.901822	+	0.432108i	$0.857770\pi$
$380$	−23.8167	−	11.4695i	−1.22177	−	0.588373i
$381$	15.1913	−	7.31574i	0.778273	−	0.374797i
$382$	−14.6082	−	64.0026i	−0.747419	−	3.27466i
$383$	6.29552	−	27.5825i	0.321686	−	1.40940i	−0.512865	−	0.858469i	$-0.671416\pi$
$383$	6.29552	−	27.5825i	0.321686	−	1.40940i	0.834552	−	0.550930i	$-0.185727\pi$
$384$	−16.6347	−	8.01084i	−0.848885	−	0.408802i
$385$	−11.9645	−	15.0030i	−0.609767	−	0.764623i
$386$	26.4827	+	33.2082i	1.34793	+	1.69025i
$387$	−1.70050	+	0.818919i	−0.0864414	+	0.0416280i
$388$	54.3153	−	68.1093i	2.75744	−	3.45772i
$389$	−27.1843			−1.37830			−0.689149	−	0.724619i	$-0.742016\pi$
$389$	−27.1843			−1.37830			−0.689149	+	0.724619i	$0.742016\pi$
$390$	−12.0033	+	15.0517i	−0.607813	+	0.762174i
$391$	−1.27204	+	5.57316i	−0.0643297	+	0.281847i
$392$	−2.62802	+	11.5141i	−0.132735	+	0.581550i
$393$	−2.83882	+	3.55977i	−0.143200	+	0.179567i
$394$	−34.1836			−1.72215
$395$	7.29115	−	9.14281i	0.366857	−	0.460025i
$396$	−12.1647	+	5.85819i	−0.611297	+	0.294385i
$397$	3.09017	+	3.87495i	0.155091	+	0.194478i	0.853306	−	0.521410i	$-0.174594\pi$
$397$	3.09017	+	3.87495i	0.155091	+	0.194478i	−0.698215	+	0.715888i	$0.746022\pi$
$398$	13.5810	+	17.0301i	0.680756	+	0.853641i
$399$	−3.49835	−	1.68471i	−0.175136	−	0.0843412i
$400$	−13.0432	+	57.1462i	−0.652162	+	2.85731i
$401$	−1.38397	−	6.06358i	−0.0691123	−	0.302801i	0.928544	−	0.371222i	$-0.121061\pi$
$401$	−1.38397	−	6.06358i	−0.0691123	−	0.302801i	−0.997657	+	0.0684210i	$0.978204\pi$
$402$	16.8458	−	8.11249i	0.840190	−	0.404614i
$403$	12.0286	+	5.79266i	0.599186	+	0.288553i
$404$	−5.28945	−	23.1746i	−0.263160	−	1.15298i
$405$	3.11062			0.154568
$406$	4.41061	+	33.9346i	0.218895	+	1.68415i
$407$	17.9540			0.889946
$408$	9.18677	+	40.2499i	0.454813	+	1.99267i
$409$	−4.17933	−	2.01266i	−0.206655	−	0.0995196i	0.327694	−	0.944784i	$-0.393729\pi$
$409$	−4.17933	−	2.01266i	−0.206655	−	0.0995196i	−0.534348	+	0.845264i	$0.679443\pi$
$410$	−57.6135	+	27.7452i	−2.84533	+	1.37024i
$411$	−4.89751	−	21.4574i	−0.241577	−	1.05842i
$412$	−12.1566	+	53.2613i	−0.598910	+	2.62400i
$413$	−10.4745	−	5.04427i	−0.515418	−	0.248212i
$414$	1.97790	+	2.48021i	0.0972087	+	0.121896i
$415$	−20.5482	−	25.7666i	−1.00867	−	1.26483i
$416$	−34.3521	+	16.5431i	−1.68425	+	0.811092i
$417$	5.04632	−	6.32789i	0.247119	−	0.309878i
$418$	−11.4309			−0.559103
$419$	8.52181	−	10.6860i	0.416318	−	0.522046i	−0.528813	−	0.848738i	$-0.677363\pi$
$419$	8.52181	−	10.6860i	0.416318	−	0.522046i	0.945131	+	0.326693i	$0.105934\pi$
$420$	−8.51081	+	37.2883i	−0.415285	+	1.81948i
$421$	2.64867	−	11.6046i	0.129088	−	0.565573i	−0.868470	−	0.495741i	$-0.834896\pi$
$421$	2.64867	−	11.6046i	0.129088	−	0.565573i	0.997559	−	0.0698322i	$-0.0222464\pi$
$422$	35.0949	−	44.0077i	1.70840	−	2.14226i
$423$	−9.30167			−0.452263
$424$	27.5633	−	34.5633i	1.33859	−	1.67854i
$425$	20.3527	−	9.80135i	0.987252	−	0.475435i
$426$	6.24444	+	7.83028i	0.302544	+	0.379378i
$427$	17.0479	+	21.3773i	0.825003	+	1.03452i
$428$	−64.2809	−	30.9560i	−3.10713	−	1.49632i
$429$	−1.33701	+	5.85781i	−0.0645513	+	0.282818i
$430$	3.50248	+	15.3454i	0.168904	+	0.740019i
$431$	20.4808	−	9.86302i	0.986524	−	0.475085i	0.130180	−	0.991490i	$-0.458444\pi$
$431$	20.4808	−	9.86302i	0.986524	−	0.475085i	0.856344	+	0.516405i	$0.172730\pi$
$432$	11.2942	+	5.43900i	0.543393	+	0.261684i
$433$	1.22623	+	5.37245i	0.0589287	+	0.258184i	0.995808	−	0.0914698i	$-0.0291565\pi$
$433$	1.22623	+	5.37245i	0.0589287	+	0.258184i	−0.936879	+	0.349653i	$0.886299\pi$
$434$	36.7494			1.76403
$435$	−2.15906	−	16.6115i	−0.103519	−	0.796459i
$436$	−27.7653			−1.32972
$437$	0.431339	+	1.88982i	0.0206337	+	0.0904023i
$438$	−5.78128	−	2.78412i	−0.276240	−	0.133030i
$439$	−18.2571	+	8.79215i	−0.871363	+	0.419626i	−0.815462	−	0.578810i	$-0.803517\pi$
$439$	−18.2571	+	8.79215i	−0.871363	+	0.419626i	−0.0559006	+	0.998436i	$0.517803\pi$
$440$	15.3955	+	67.4520i	0.733950	+	3.21565i
$441$	0.307525	−	1.34735i	0.0146440	−	0.0641597i
$442$	26.9389	+	12.9731i	1.28135	+	0.617067i
$443$	21.1350	+	26.5024i	1.00415	+	1.25917i	0.965633	+	0.259911i	$0.0836933\pi$
$443$	21.1350	+	26.5024i	1.00415	+	1.25917i	0.0385212	+	0.999258i	$0.487735\pi$
$444$	−22.3114	−	27.9776i	−1.05885	−	1.32776i
$445$	15.9820	−	7.69650i	0.757617	−	0.364849i
$446$	−35.4487	+	44.4512i	−1.67854	+	2.10483i
$447$	−0.743685			−0.0351751
$448$	−28.3855	+	35.5943i	−1.34109	+	1.68167i
$449$	−7.17733	+	31.4459i	−0.338719	+	1.48403i	0.463018	+	0.886349i	$0.346766\pi$
$449$	−7.17733	+	31.4459i	−0.338719	+	1.48403i	−0.801737	+	0.597677i	$0.796091\pi$
$450$	2.78953	−	12.2217i	0.131499	−	0.576137i
$451$	−12.4432	+	15.6033i	−0.585930	+	0.734733i
$452$	−56.0148			−2.63472
$453$	10.7789	−	13.5163i	0.506437	−	0.635052i
$454$	25.8558	−	12.4515i	1.21347	−	0.584378i
$455$	10.6121	+	13.3072i	0.497504	+	0.623851i
$456$	8.72851	+	10.9452i	0.408750	+	0.512556i
$457$	23.5438	+	11.3381i	1.10133	+	0.530375i	0.894078	−	0.447912i	$-0.147832\pi$
$457$	23.5438	+	11.3381i	1.10133	+	0.530375i	0.207257	+	0.978287i	$0.433546\pi$
$458$	−8.35546	+	36.6076i	−0.390425	+	1.71056i
$459$	−1.07502	−	4.70995i	−0.0501774	−	0.219842i
$460$	17.2030	−	8.28453i	0.802095	−	0.386268i
$461$	11.2947	+	5.43923i	0.526046	+	0.253330i	0.678006	−	0.735056i	$-0.262844\pi$
$461$	11.2947	+	5.43923i	0.526046	+	0.253330i	−0.151960	+	0.988387i	$0.548559\pi$
$462$	3.68027	+	16.1243i	0.171222	+	0.750171i
$463$	−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
$465$	−17.9893			−0.834236
$466$	−7.38860	−	32.3716i	−0.342270	−	1.49958i
$467$	6.22496	+	2.99778i	0.288057	+	0.138721i	0.572332	−	0.820022i	$-0.306039\pi$
$467$	6.22496	+	2.99778i	0.288057	+	0.138721i	−0.284276	+	0.958743i	$0.591753\pi$
$468$	10.7897	−	5.19603i	0.498753	−	0.240187i
$469$	−3.67834	−	16.1159i	−0.169850	−	0.744161i
$470$	−17.2611	+	75.6259i	−0.796196	+	3.48836i
$471$	−0.359744	−	0.173243i	−0.0165761	−	0.00798264i
$472$	26.1344	+	32.7714i	1.20293	+	1.50843i
$473$	3.06284	+	3.84068i	0.140829	+	0.176595i
$474$	−9.08072	+	4.37304i	−0.417091	+	0.200861i
$475$	4.77596	−	5.98886i	0.219136	−	0.274788i
$476$	59.4015			2.72266
$477$	−3.22539	+	4.04451i	−0.147681	+	0.185186i
$478$	5.31150	−	23.2712i	0.242942	−	1.06440i
$479$	3.38908	−	14.8485i	0.154851	−	0.678446i	−0.836583	−	0.547840i	$-0.815450\pi$
$479$	3.38908	−	14.8485i	0.154851	−	0.678446i	0.991434	−	0.130607i	$-0.0416925\pi$
$480$	32.0319	−	40.1668i	1.46205	−	1.83335i
$481$	−15.9246			−0.726101
$482$	43.7108	−	54.8116i	1.99097	−	2.49660i
$483$	2.52689	−	1.21689i	0.114977	−	0.0553702i
$484$	−13.6681	−	17.1392i	−0.621275	−	0.779054i
$485$	32.5691	+	40.8404i	1.47889	+	1.85447i
$486$	−2.41546	−	1.16323i	−0.109568	−	0.0527650i
$487$	7.04525	−	30.8672i	0.319251	−	1.39873i	−0.519620	−	0.854397i	$-0.673927\pi$
$487$	7.04525	−	30.8672i	0.319251	−	1.39873i	0.838871	−	0.544331i	$-0.183216\pi$
$488$	−21.9366	−	96.1104i	−0.993022	−	4.35071i
$489$	8.93169	−	4.30127i	0.403905	−	0.194510i
$490$	−10.3838	−	5.00057i	−0.469092	−	0.225903i
$491$	−2.38715	−	10.4588i	−0.107731	−	0.471998i	−0.999798	−	0.0200962i	$-0.993603\pi$
$491$	−2.38715	−	10.4588i	−0.107731	−	0.471998i	0.892067	−	0.451902i	$-0.149254\pi$
$492$	39.7777			1.79332
$493$	−24.4061	+	9.00999i	−1.09920	+	0.405789i
$494$	10.1388			0.456168
$495$	−1.80154	−	7.89308i	−0.0809733	−	0.354767i
$496$	−65.3167	−	31.4549i	−2.93281	−	1.41237i
$497$	7.97763	−	3.84182i	0.357846	−	0.172329i
$498$	6.32062	+	27.6924i	0.283234	+	1.24093i
$499$	2.17395	−	9.52472i	0.0973196	−	0.426385i	−0.902673	−	0.430328i	$-0.858398\pi$
$499$	2.17395	−	9.52472i	0.0973196	−	0.426385i	0.999992	+	0.00394299i	$0.00125509\pi$
$500$	4.71135	+	2.26887i	0.210698	+	0.101467i
$501$	7.30666	+	9.16227i	0.326438	+	0.409340i
$502$	−6.47980	−	8.12541i	−0.289208	−	0.362655i
$503$	21.8843	−	10.5389i	0.975771	−	0.469907i	0.123123	−	0.992391i	$-0.460709\pi$
$503$	21.8843	−	10.5389i	0.975771	−	0.469907i	0.852649	+	0.522485i	$0.174995\pi$
$504$	12.6290	−	15.8362i	0.562540	−	0.705403i
$505$	14.2536			0.634275
$506$	5.14793	−	6.45530i	0.228853	−	0.286973i
$507$	−1.70689	+	7.47836i	−0.0758055	+	0.332126i
$508$	−19.4634	+	85.2747i	−0.863548	+	3.78345i
$509$	−2.52048	+	3.16058i	−0.111718	+	0.140090i	−0.834547	−	0.550937i	$-0.814270\pi$
$509$	−2.52048	+	3.16058i	−0.111718	+	0.140090i	0.722828	+	0.691028i	$0.242842\pi$
$510$	−40.2885			−1.78400
$511$	−3.53707	+	4.43534i	−0.156471	+	0.196208i
$512$	−6.49796	+	3.12925i	−0.287172	+	0.138295i
$513$	−1.02139	−	1.28078i	−0.0450955	−	0.0565479i
$514$	2.70175	+	3.38789i	0.119169	+	0.149433i
$515$	−29.5144	−	14.2134i	−1.30056	−	0.626316i
$516$	2.17872	−	9.54559i	0.0959127	−	0.420221i
$517$	5.38715	+	23.6027i	0.236927	+	1.03804i
$518$	−39.4934	+	19.0190i	−1.73524	+	0.835649i
$519$	7.33695	+	3.53329i	0.322056	+	0.155094i
$520$	−13.6553	−	59.8278i	−0.598825	−	2.62362i
$521$	−20.3240			−0.890412			−0.445206	−	0.895428i	$-0.646870\pi$
$521$	−20.3240			−0.890412			−0.445206	+	0.895428i	$0.646870\pi$
$522$	−4.53536	+	13.7066i	−0.198507	+	0.599920i
$523$	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
$525$	−9.98549	−	4.80876i	−0.435803	−	0.209871i
$526$	−54.7398	+	26.3613i	−2.38677	+	1.14941i
$527$	6.21703	+	27.2386i	0.270818	+	1.18653i
$528$	7.26012	−	31.8087i	0.315956	−	1.38430i
$529$	19.4608	+	9.37183i	0.846122	+	0.407471i
$530$	26.8980	+	33.7290i	1.16837	+	1.46509i
$531$	−3.05818	−	3.83484i	−0.132714	−	0.166418i
$532$	18.1479	−	8.73955i	0.786810	−	0.378908i
$533$	11.0368	−	13.8397i	0.478056	−	0.599463i
$534$	−15.2885			−0.661597
$535$	26.6738	−	33.4479i	1.15321	−	1.44608i
$536$	−13.2620	+	58.1047i	−0.572832	+	2.50974i
$537$	2.39845	−	10.5083i	0.103501	−	0.453466i
$538$	8.72587	−	10.9419i	0.376199	−	0.471739i
$539$	−3.59696			−0.154932
$540$	−10.0609	+	12.6160i	−0.432954	+	0.542907i
$541$	24.3124	−	11.7082i	1.04527	−	0.503376i	0.169212	−	0.985580i	$-0.445878\pi$
$541$	24.3124	−	11.7082i	1.04527	−	0.503376i	0.876059	+	0.482203i	$0.160163\pi$
$542$	−2.50629	−	3.14279i	−0.107654	−	0.134994i
$543$	−12.8517	−	16.1155i	−0.551518	−	0.691582i
$544$	−71.8887	−	34.6198i	−3.08220	−	1.48431i
$545$	3.70474	−	16.2315i	0.158694	−	0.695282i
$546$	−3.26429	−	14.3018i	−0.139699	−	0.612059i
$547$	−7.87494	+	3.79237i	−0.336708	+	0.162150i	−0.594596	−	0.804025i	$-0.702688\pi$
$547$	−7.87494	+	3.79237i	−0.336708	+	0.162150i	0.257887	+	0.966175i	$0.416974\pi$
$548$	102.867	+	49.5383i	4.39427	+	2.11617i
$549$	2.56697	+	11.2466i	0.109556	+	0.479994i
$550$	−32.6277			−1.39125
$551$	−6.13075	+	6.34346i	−0.261179	+	0.270240i
$552$	−10.1119			−0.430392
$553$	1.98281	+	8.68727i	0.0843177	+	0.369420i
$554$	5.26857	+	2.53721i	0.223840	+	0.107796i
$555$	19.3326	−	9.31009i	0.820623	−	0.395191i
$556$	9.34285	+	40.9337i	0.396225	+	1.73598i
$557$	6.30376	−	27.6186i	0.267099	−	1.17024i	−0.646272	−	0.763107i	$-0.723673\pi$
$557$	6.30376	−	27.6186i	0.267099	−	1.17024i	0.913371	−	0.407129i	$-0.133470\pi$
$558$	13.9691	+	6.72717i	0.591360	+	0.284784i
$559$	−2.71664	−	3.40656i	−0.114902	−	0.144082i
$560$	−57.6252	−	72.2597i	−2.43511	−	3.05353i
$561$	−11.3287	+	5.45562i	−0.478299	+	0.230337i
$562$	28.7965	−	36.1097i	1.21471	−	1.52319i
$563$	−1.24481			−0.0524623			−0.0262312	−	0.999656i	$-0.508351\pi$
$563$	−1.24481			−0.0524623			−0.0262312	+	0.999656i	$0.508351\pi$
$564$	30.0852	−	37.7257i	1.26682	−	1.58854i
$565$	7.47408	−	32.7461i	0.314437	−	1.37764i
$566$	−6.81907	+	29.8763i	−0.286627	+	1.25579i
$567$	−1.47782	+	1.85312i	−0.0620624	+	0.0778238i
$568$	−31.9243			−1.33951
$569$	−5.14541	+	6.45214i	−0.215707	+	0.270488i	−0.877899	−	0.478847i	$-0.841055\pi$
$569$	−5.14541	+	6.45214i	−0.215707	+	0.270488i	0.662192	+	0.749334i	$0.269626\pi$
$570$	−12.3086	+	5.92752i	−0.515551	+	0.248276i
$571$	17.3342	+	21.7364i	0.725415	+	0.909642i	0.998631	−	0.0523110i	$-0.0166587\pi$
$571$	17.3342	+	21.7364i	0.725415	+	0.909642i	−0.273216	+	0.961953i	$0.588087\pi$
$572$	−19.4337	−	24.3691i	−0.812563	−	1.01892i
$573$	−22.0620	−	10.6245i	−0.921651	−	0.443844i
$574$	10.8425	−	47.5041i	0.452557	−	1.98278i
$575$	1.23119	+	5.39420i	0.0513442	+	0.224954i
$576$	−17.3056	+	8.33394i	−0.721067	+	0.347247i
$577$	−6.48400	−	3.12253i	−0.269932	−	0.129993i	0.294022	−	0.955799i	$-0.405006\pi$
$577$	−6.48400	−	3.12253i	−0.269932	−	0.129993i	−0.563954	+	0.825806i	$0.690721\pi$
$578$	3.78182	+	16.5692i	0.157303	+	0.689190i
$579$	15.8432			0.658419
$580$	74.3559	+	44.9712i	3.08746	+	1.86733i
$581$	25.1124			1.04184
$582$	−10.0182	−	43.8928i	−0.415270	−	1.81942i
$583$	12.1308	+	5.84190i	0.502407	+	0.241947i
$584$	18.4281	−	8.87453i	0.762562	−	0.367231i
$585$	1.59791	+	7.00092i	0.0660656	+	0.289452i
$586$	−3.05714	+	13.3942i	−0.126289	+	0.553310i
$587$	−7.62256	−	3.67083i	−0.314617	−	0.151511i	0.269911	−	0.962885i	$-0.413006\pi$
$587$	−7.62256	−	3.67083i	−0.314617	−	0.151511i	−0.584527	+	0.811374i	$0.698720\pi$
$588$	4.46993	+	5.60512i	0.184337	+	0.231151i
$589$	5.90691	+	7.40703i	0.243390	+	0.305201i
$590$	−36.8537	+	17.7478i	−1.51724	+	0.730666i
$591$	−7.94981	+	9.96875i	−0.327012	+	0.410060i
$592$	86.4728			3.55401
$593$	−17.9522	+	22.5114i	−0.737210	+	0.924433i	−0.999174	−	0.0406452i	$-0.987059\pi$
$593$	−17.9522	+	22.5114i	−0.737210	+	0.924433i	0.261963	+	0.965078i	$0.415630\pi$
$594$	−1.55270	+	6.80284i	−0.0637082	+	0.279124i
$595$	−7.92596	+	34.7259i	−0.324933	+	1.42362i
$596$	2.40537	−	3.01623i	0.0985277	−	0.123550i
$597$	8.12481			0.332526
$598$	−4.56606	+	5.72565i	−0.186720	+	0.234139i
$599$	2.23432	−	1.07599i	0.0912920	−	0.0439639i	−0.387681	−	0.921794i	$-0.626724\pi$
$599$	2.23432	−	1.07599i	0.0912920	−	0.0439639i	0.478973	+	0.877830i	$0.341009\pi$
$600$	24.9142	+	31.2414i	1.01712	+	1.27542i
$601$	−24.7528	−	31.0390i	−1.00969	−	1.26611i	−0.963650	−	0.267167i	$-0.913912\pi$
$601$	−24.7528	−	31.0390i	−1.00969	−	1.26611i	−0.0460366	−	0.998940i	$-0.514659\pi$
$602$	−10.8058	−	5.20382i	−0.440413	−	0.212092i
$603$	1.55189	−	6.79927i	0.0631979	−	0.276888i
$604$	19.9563	+	87.4341i	0.812009	+	3.55764i
$605$	11.8433	−	5.70341i	0.481497	−	0.231877i
$606$	−11.0682	−	5.33016i	−0.449615	−	0.216523i
$607$	−7.86688	−	34.4671i	−0.319307	−	1.39898i	−0.838772	−	0.544483i	$-0.816726\pi$
$607$	−7.86688	−	34.4671i	−0.319307	−	1.39898i	0.519465	−	0.854492i	$-0.326131\pi$
$608$	−27.0564			−1.09728
$609$	10.9219	+	6.60566i	0.442576	+	0.267675i
$610$	96.2026			3.89513
$611$	−4.77824	−	20.9348i	−0.193307	−	0.846933i
$612$	22.5796	+	10.8738i	0.912726	+	0.439546i
$613$	−7.29240	+	3.51183i	−0.294537	+	0.141842i	−0.575317	−	0.817931i	$-0.695121\pi$
$613$	−7.29240	+	3.51183i	−0.294537	+	0.141842i	0.280780	+	0.959772i	$0.409407\pi$
$614$	2.02257	+	8.86146i	0.0816243	+	0.357619i
$615$	−5.30756	+	23.2539i	−0.214021	+	0.937689i
$616$	−47.4981	−	22.8739i	−1.91375	−	0.921615i
$617$	17.0599	+	21.3924i	0.686805	+	0.861227i	0.995961	−	0.0897847i	$-0.0286179\pi$
$617$	17.0599	+	21.3924i	0.686805	+	0.861227i	−0.309156	+	0.951011i	$0.600046\pi$
$618$	17.6034	+	22.0740i	0.708113	+	0.887946i
$619$	−24.4911	+	11.7943i	−0.984382	+	0.474053i	−0.855610	−	0.517621i	$-0.826818\pi$
$619$	−24.4911	+	11.7943i	−0.984382	+	0.474053i	−0.128772	+	0.991674i	$0.541103\pi$
$620$	58.1845	−	72.9611i	2.33675	−	2.93019i
$621$	1.18327			0.0474832
$622$	−28.6140	+	35.8809i	−1.14732	+	1.43869i
$623$	−3.00770	+	13.1776i	−0.120501	+	0.527950i
$624$	−6.43951	+	28.2133i	−0.257787	+	1.12944i
$625$	−16.5320	+	20.7305i	−0.661280	+	0.829219i
$626$	3.88251			0.155176
$627$	−2.65839	+	3.33352i	−0.106166	+	0.133128i
$628$	1.86619	−	0.898710i	0.0744691	−	0.0358624i
$629$	−20.7781	−	26.0550i	−0.828479	−	1.03888i
$630$	12.3242	+	15.4540i	0.491006	+	0.615702i
$631$	−17.7488	−	8.54737i	−0.706568	−	0.340265i	0.0458525	−	0.998948i	$-0.485400\pi$
$631$	−17.7488	−	8.54737i	−0.706568	−	0.340265i	−0.752421	+	0.658683i	$0.771114\pi$
$632$	7.14890	−	31.3214i	0.284368	−	1.24590i
$633$	−4.67192	−	20.4690i	−0.185692	−	0.813571i
$634$	−42.3115	+	20.3761i	−1.68040	+	0.809240i
$635$	−47.2543	−	22.7565i	−1.87523	−	0.903062i
$636$	−5.97155	−	26.1631i	−0.236787	−	1.03743i
$637$	3.19040			0.126408
$638$	37.4066	+	3.57002i	1.48094	+	0.141338i
$639$	3.73571			0.147782
$640$	12.7797	+	55.9917i	0.505164	+	2.21327i
$641$	−0.252515	−	0.121605i	−0.00997374	−	0.00480310i	0.428890	−	0.903357i	$-0.358905\pi$
$641$	−0.252515	−	0.121605i	−0.00997374	−	0.00480310i	−0.438864	+	0.898554i	$0.644619\pi$
$642$	−33.2208	+	15.9983i	−1.31112	+	0.631402i
$643$	10.4808	+	45.9192i	0.413321	+	1.81088i	0.568137	+	0.822934i	$0.307664\pi$
$643$	10.4808	+	45.9192i	0.413321	+	1.81088i	−0.154817	+	0.987943i	$0.549479\pi$
$644$	−3.23750	+	14.1844i	−0.127575	+	0.558944i
$645$	5.28961	+	2.54734i	0.208278	+	0.100302i
$646$	13.2290	+	16.5886i	0.520487	+	0.652670i
$647$	−0.681877	−	0.855046i	−0.0268073	−	0.0336153i	0.768247	−	0.640153i	$-0.221129\pi$
$647$	−0.681877	−	0.855046i	−0.0268073	−	0.0336153i	−0.795054	+	0.606538i	$0.792558\pi$
$648$	7.69942	−	3.70785i	0.302462	−	0.145658i
$649$	−7.95959	+	9.98101i	−0.312441	+	0.391789i
$650$	28.9398			1.13511
$651$	8.54651	−	10.7170i	0.334964	−	0.420032i
$652$	−11.4435	+	50.1371i	−0.448161	+	1.96352i
$653$	6.63281	−	29.0602i	0.259562	−	1.13722i	−0.662160	−	0.749363i	$-0.730360\pi$
$653$	6.63281	−	29.0602i	0.259562	−	1.13722i	0.921721	−	0.387852i	$-0.126783\pi$
$654$	−8.94664	+	11.2187i	−0.349841	+	0.438687i
$655$	14.1630			0.553395
$656$	−59.9311	+	75.1513i	−2.33992	+	2.93416i
$657$	−2.15642	+	1.03848i	−0.0841299	+	0.0405148i
$658$	−36.8529	−	46.2121i	−1.43668	−	1.80153i
$659$	−20.7854	−	26.0640i	−0.809683	−	1.01531i	−0.999439	−	0.0334791i	$-0.989341\pi$
$659$	−20.7854	−	26.0640i	−0.809683	−	1.01531i	0.189756	−	0.981831i	$-0.439230\pi$
$660$	37.8396	+	18.2226i	1.47290	+	0.709313i
$661$	−0.544903	+	2.38738i	−0.0211943	+	0.0928581i	−0.984419	−	0.175839i	$-0.943736\pi$
$661$	−0.544903	+	2.38738i	−0.0211943	+	0.0928581i	0.963225	+	0.268698i	$0.0865932\pi$
$662$	6.22082	+	27.2552i	0.241779	+	1.05930i
$663$	10.0482	−	4.83897i	0.390241	−	0.187930i
$664$	−81.5748	−	39.2844i	−3.16572	−	1.52453i
$665$	2.68764	+	11.7753i	0.104222	+	0.456627i
$666$	−18.4937			−0.716617
$667$	−0.821302	−	6.31898i	−0.0318009	−	0.244672i
$668$	−60.7929			−2.35215
$669$	4.71901	+	20.6753i	0.182447	+	0.799355i
$670$	−52.4007	−	25.2348i	−2.02442	−	0.974907i
$671$	27.0512	−	13.0272i	1.04430	−	0.502908i
$672$	8.71102	+	38.1655i	0.336035	+	1.47226i
$673$	−2.49804	+	10.9446i	−0.0962924	+	0.421884i	−0.999980	−	0.00630766i	$-0.997992\pi$
$673$	−2.49804	+	10.9446i	−0.0962924	+	0.421884i	0.903688	+	0.428192i	$0.140849\pi$
$674$	−77.7809	−	37.4573i	−2.99601	−	1.44280i
$675$	−2.91540	−	3.65580i	−0.112214	−	0.140712i
$676$	−24.8100	−	31.1107i	−0.954229	−	1.19657i
$677$	4.61715	−	2.22350i	0.177451	−	0.0854561i	−0.343049	−	0.939318i	$-0.611460\pi$
$677$	4.61715	−	2.22350i	0.177451	−	0.0854561i	0.520500	+	0.853861i	$0.325745\pi$
$678$	−18.0493	+	22.6331i	−0.693179	+	0.869219i
$679$	−39.8035			−1.52752
$680$	80.0697	−	100.404i	3.07053	−	3.85032i
$681$	2.38193	−	10.4359i	0.0912757	−	0.399905i
$682$	8.97961	−	39.3422i	0.343847	−	1.50649i
$683$	18.4315	−	23.1123i	0.705260	−	0.884368i	−0.292144	−	0.956374i	$-0.594369\pi$
$683$	18.4315	−	23.1123i	0.705260	−	0.884368i	0.997404	+	0.0720063i	$0.0229402\pi$
$684$	8.49816			0.324935
$685$	−42.6855	+	53.5260i	−1.63093	+	2.04512i
$686$	47.9887	−	23.1101i	1.83222	−	0.882349i
$687$	8.73249	+	10.9502i	0.333165	+	0.417776i
$688$	14.7517	+	18.4981i	0.562404	+	0.705232i
$689$	−10.7597	−	5.18158i	−0.409911	−	0.197403i
$690$	2.19580	−	9.62044i	0.0835928	−	0.366244i
$691$	−9.83685	−	43.0981i	−0.374211	−	1.63953i	−0.714810	−	0.699319i	$-0.753487\pi$
$691$	−9.83685	−	43.0981i	−0.374211	−	1.63953i	0.340599	−	0.940209i	$-0.389370\pi$
$692$	−38.0608	+	18.3291i	−1.44685	+	0.696769i
$693$	5.55812	+	2.67665i	0.211135	+	0.101677i
$694$	4.15557	+	18.2068i	0.157743	+	0.691119i
$695$	−25.1763			−0.954992
$696$	−25.1449	−	38.5432i	−0.953116	−	1.46098i
$697$	37.0443			1.40315
$698$	8.33491	+	36.5176i	0.315481	+	1.38221i
$699$	−11.1586	−	5.37371i	−0.422058	−	0.203252i
$700$	51.8003	−	24.9457i	1.95787	−	0.942859i
$701$	5.71682	+	25.0470i	0.215921	+	0.946013i	0.960457	+	0.278430i	$0.0898139\pi$
$701$	5.71682	+	25.0470i	0.215921	+	0.946013i	−0.744535	+	0.667583i	$0.767329\pi$
$702$	1.37720	−	6.03391i	0.0519791	−	0.227735i
$703$	−10.1814	−	4.90308i	−0.383997	−	0.184923i
$704$	31.1698	+	39.0857i	1.17475	+	1.47310i
$705$	18.0400	+	22.6215i	0.679426	+	0.851974i
$706$	62.4210	−	30.0604i	2.34925	−	1.13134i
$707$	−6.77168	+	8.49142i	−0.254675	+	0.319353i
$708$	25.4447			0.956269
$709$	11.3053	−	14.1764i	0.424579	−	0.532405i	−0.522827	−	0.852439i	$-0.675123\pi$
$709$	11.3053	−	14.1764i	0.424579	−	0.532405i	0.947406	+	0.320033i	$0.103694\pi$
$710$	6.93236	−	30.3727i	0.260167	−	1.13987i
$711$	−0.836548	+	3.66516i	−0.0313730	+	0.137454i
$712$	30.3844	−	38.1009i	1.13871	−	1.42789i
$713$	−6.84312			−0.256277
$714$	19.1405	−	24.0015i	0.716317	−	0.898233i
$715$	16.8391	−	8.10929i	0.629747	−	0.303270i
$716$	34.8619	+	43.7155i	1.30285	+	1.63372i
$717$	−5.55118	−	6.96096i	−0.207312	−	0.259962i
$718$	−42.3756	−	20.4070i	−1.58144	−	0.761583i
$719$	−1.22528	+	5.36832i	−0.0456954	+	0.200205i	−0.992623	−	0.121243i	$-0.961312\pi$
$719$	−1.22528	+	5.36832i	−0.0456954	+	0.200205i	0.946928	+	0.321447i	$0.104169\pi$
$720$	−8.67687	−	38.0159i	−0.323368	−	1.41677i
$721$	22.4894	−	10.8303i	0.837548	−	0.403342i
$722$	−39.4116	−	18.9796i	−1.46675	−	0.706348i
$723$	−5.81888	−	25.4942i	−0.216406	−	0.948138i
$724$	106.928			3.97396
$725$	−17.4993	+	18.1064i	−0.649908	+	0.672456i
$726$	−11.3294			−0.420472
$727$	6.13737	+	26.8896i	0.227622	+	0.997279i	0.951572	+	0.307426i	$0.0994677\pi$
$727$	6.13737	+	26.8896i	0.227622	+	0.997279i	−0.723950	+	0.689853i	$0.757675\pi$
$728$	42.1293	+	20.2884i	1.56142	+	0.751939i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	4.44152	+	19.4596i	0.164388	+	0.720231i
$731$	2.02900	−	8.88963i	0.0750453	−	0.328795i
$732$	−53.9165	−	25.9648i	−1.99281	−	0.959688i
$733$	−26.6783	−	33.4535i	−0.985384	−	1.23563i	−0.971820	−	0.235724i	$-0.924254\pi$
$733$	−26.6783	−	33.4535i	−0.985384	−	1.23563i	−0.0135639	−	0.999908i	$-0.504318\pi$
$734$	−49.7502	−	62.3848i	−1.83631	−	2.30267i
$735$	−3.87316	+	1.86521i	−0.142864	+	0.0687995i
$736$	12.1849	−	15.2794i	0.449142	−	0.563206i
$737$	−18.1517			−0.668627
$738$	12.8173	−	16.0724i	0.471812	−	0.591633i
$739$	−6.66662	+	29.2084i	−0.245236	+	1.07445i	0.690939	+	0.722913i	$0.257197\pi$
$739$	−6.66662	+	29.2084i	−0.245236	+	1.07445i	−0.936175	+	0.351535i	$0.885660\pi$
$740$	−24.7693	+	108.521i	−0.910538	+	3.98933i
$741$	2.35791	−	2.95673i	0.0866200	−	0.108618i
$742$	−32.8726			−1.20679
$743$	0.969337	−	1.21551i	0.0355615	−	0.0445928i	−0.763733	−	0.645533i	$-0.776635\pi$
$743$	0.969337	−	1.21551i	0.0355615	−	0.0445928i	0.799294	+	0.600940i	$0.205207\pi$
$744$	−44.5273	+	21.4432i	−1.63245	+	0.786147i
$745$	1.44233	+	1.80863i	0.0528429	+	0.0662630i
$746$	−32.2534	−	40.4445i	−1.18088	−	1.48078i
$747$	9.54570	+	4.59697i	0.349259	+	0.168194i
$748$	14.5146	−	63.5925i	0.530706	−	2.32517i
$749$	7.25389	+	31.7814i	0.265051	+	1.16127i
$750$	2.43486	−	1.17257i	0.0889084	−	0.0428160i
$751$	37.8839	+	18.2439i	1.38240	+	0.665731i	0.969511	−	0.245048i	$-0.0788037\pi$
$751$	37.8839	+	18.2439i	1.38240	+	0.665731i	0.412894	+	0.910779i	$0.364518\pi$
$752$	25.9464	+	113.679i	0.946169	+	4.14544i
$753$	−3.87652			−0.141268
$754$	−33.1785	−	3.16650i	−1.20829	−	0.115317i
$755$	−53.7765			−1.95713
$756$	−2.73605	−	11.9874i	−0.0995093	−	0.435979i
$757$	24.4696	+	11.7839i	0.889362	+	0.428294i	0.822035	−	0.569437i	$-0.192839\pi$
$757$	24.4696	+	11.7839i	0.889362	+	0.428294i	0.0673267	+	0.997731i	$0.478553\pi$
$758$	−20.7470	+	9.99124i	−0.753566	+	0.362898i
$759$	−0.685304	−	3.00251i	−0.0248750	−	0.108984i
$760$	9.69009	−	42.4551i	0.351497	−	1.54001i
$761$	31.5591	+	15.1980i	1.14402	+	0.550929i	0.907231	−	0.420633i	$-0.138192\pi$
$761$	31.5591	+	15.1980i	1.14402	+	0.550929i	0.236785	+	0.971562i	$0.423906\pi$
$762$	28.1841	+	35.3418i	1.02100	+	1.28030i
$763$	7.90970	+	9.91846i	0.286351	+	0.359072i
$764$	114.448	−	55.1151i	4.14057	−	1.99399i
$765$	−9.36957	+	11.7491i	−0.338757	+	0.424788i
$766$	75.8493

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.596570 + 2.61374i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-4.67383 + 2.25080i) q^{4} +(-0.692177 - 3.03263i) q^{5} +(-0.596570 + 2.61374i) q^{6} +(2.13550 + 1.02840i) q^{7} +(-5.32817 - 6.68131i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(0.596570 + 2.61374i) q^{2} +(0.900969 + 0.433884i) q^{3} +(-4.67383 + 2.25080i) q^{4} +(-0.692177 - 3.03263i) q^{5} +(-0.596570 + 2.61374i) q^{6} +(2.13550 + 1.02840i) q^{7} +(-5.32817 - 6.68131i) q^{8} +(0.623490 + 0.781831i) q^{9} +(7.51358 - 3.61835i) q^{10} +(1.62277 - 2.03489i) q^{11} -5.18756 q^{12} +(-1.43935 + 1.80488i) q^{13} +(-1.41401 + 6.19518i) q^{14} +(0.692177 - 3.03263i) q^{15} +(7.81583 - 9.80074i) q^{16} -4.83107 q^{17} +(-1.67155 + 2.09606i) q^{18} +(-1.47595 + 0.710781i) q^{19} +(10.0609 + 12.6160i) q^{20} +(1.47782 + 1.85312i) q^{21} +(6.28677 + 3.02755i) q^{22} +(0.263303 - 1.15361i) q^{23} +(-1.90160 - 8.33146i) q^{24} +(-4.21288 + 2.02881i) q^{25} +(-5.57617 - 2.68534i) q^{26} +(0.222521 + 0.974928i) q^{27} -12.2957 q^{28} +(5.05191 - 1.86501i) q^{29} +8.33945 q^{30} +(-1.28688 - 5.63821i) q^{31} +(14.8805 + 7.16606i) q^{32} +(2.34497 - 1.12928i) q^{33} +(-2.88207 - 12.6272i) q^{34} +(1.64062 - 7.18803i) q^{35} +(-4.67383 - 2.25080i) q^{36} +(4.30094 + 5.39321i) q^{37} +(-2.73831 - 3.43373i) q^{38} +(-2.07992 + 1.00163i) q^{39} +(-16.5739 + 20.7830i) q^{40} -7.66791 q^{41} +(-3.96197 + 4.96815i) q^{42} +(-0.419989 + 1.84009i) q^{43} +(-3.00442 + 13.1632i) q^{44} +(1.93944 - 2.43198i) q^{45} +3.17231 q^{46} +(-5.79950 + 7.27234i) q^{47} +(11.2942 - 5.43900i) q^{48} +(-0.861665 - 1.08049i) q^{49} +(-7.81608 - 9.80105i) q^{50} +(-4.35265 - 2.09612i) q^{51} +(2.66483 - 11.6754i) q^{52} +(1.15113 + 5.04343i) q^{53} +(-2.41546 + 1.16323i) q^{54} +(-7.29430 - 3.51275i) q^{55} +(-4.50723 - 19.7475i) q^{56} -1.63818 q^{57} +(7.88847 + 12.0918i) q^{58} -4.90494 q^{59} +(3.59071 + 15.7319i) q^{60} +(10.3934 + 5.00522i) q^{61} +(13.9691 - 6.72717i) q^{62} +(0.527426 + 2.31080i) q^{63} +(-4.27413 + 18.7262i) q^{64} +(6.46982 + 3.11570i) q^{65} +(4.35058 + 5.45546i) q^{66} +(-4.34830 - 5.45260i) q^{67} +(22.5796 - 10.8738i) q^{68} +(0.737759 - 0.925121i) q^{69} +19.7664 q^{70} +(2.32918 - 2.92070i) q^{71} +(1.90160 - 8.33146i) q^{72} +(-0.532592 + 2.33344i) q^{73} +(-11.5306 + 14.4590i) q^{74} -4.67594 q^{75} +(5.29852 - 6.64413i) q^{76} +(5.55812 - 2.67665i) q^{77} +(-3.85883 - 4.83882i) q^{78} +(2.34395 + 2.93923i) q^{79} +(-35.1319 - 16.9187i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-4.57445 - 20.0420i) q^{82} +(9.54570 - 4.59697i) q^{83} +(-11.0780 - 5.33491i) q^{84} +(3.34396 + 14.6508i) q^{85} -5.06009 q^{86} +(5.36081 + 0.511626i) q^{87} -22.2421 q^{88} +(1.26895 + 5.55963i) q^{89} +(7.51358 + 3.61835i) q^{90} +(-4.92988 + 2.37411i) q^{91} +(1.36590 + 5.98440i) q^{92} +(1.28688 - 5.63821i) q^{93} +(-22.4678 - 10.8199i) q^{94} +(3.17715 + 3.98402i) q^{95} +(10.2976 + 12.9128i) q^{96} +(-15.1300 + 7.28624i) q^{97} +(2.31009 - 2.89676i) q^{98} +2.60272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9	\( 18 q - 2 q^{2} + 3 q^{3} - 6 q^{4} - 7 q^{5} + 2 q^{6} - 4 q^{7} - 3 q^{8} - 3 q^{9} + 6 q^{10} - 6 q^{11} - 22 q^{12} - 11 q^{13} - 2 q^{14} + 7 q^{15} + 18 q^{16} - 32 q^{17} - 2 q^{18} + 2 q^{19} + 51 q^{20} + 4 q^{21} + 20 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 3 q^{26} + 3 q^{27} - 48 q^{28} - 10 q^{29} + 8 q^{30} + 8 q^{31} + 55 q^{32} - 8 q^{33} + 6 q^{34} + 31 q^{35} - 6 q^{36} + 20 q^{37} - 20 q^{38} - 10 q^{39} - 59 q^{40} - 68 q^{41} - 19 q^{42} - 3 q^{43} - 10 q^{44} + 14 q^{45} - 12 q^{46} + 19 q^{47} + 24 q^{48} + 17 q^{49} + 23 q^{50} + 11 q^{51} - 4 q^{52} - q^{53} - 5 q^{54} + 3 q^{55} + 7 q^{56} - 2 q^{57} - 30 q^{58} + 20 q^{59} + 47 q^{60} + 24 q^{61} + 79 q^{62} + 3 q^{63} - 23 q^{64} + 6 q^{65} + 50 q^{66} - 14 q^{67} - 8 q^{68} - 8 q^{69} + 28 q^{70} - 28 q^{71} + 4 q^{72} + 43 q^{73} - 47 q^{74} - 18 q^{75} + 19 q^{76} + 26 q^{77} - 11 q^{78} + 9 q^{79} - 74 q^{80} - 3 q^{81} - 17 q^{82} + 8 q^{83} - 15 q^{84} - 21 q^{85} - 140 q^{86} - 11 q^{87} - 58 q^{88} - 6 q^{89} + 6 q^{90} - 15 q^{91} + 11 q^{92} - 8 q^{93} + 6 q^{94} - 16 q^{95} + 36 q^{96} - 81 q^{97} - 11 q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + 3 * q^3 - 6 * q^4 - 7 * q^5 + 2 * q^6 - 4 * q^7 - 3 * q^8 - 3 * q^9 + 6 * q^10 - 6 * q^11 - 22 * q^12 - 11 * q^13 - 2 * q^14 + 7 * q^15 + 18 * q^16 - 32 * q^17 - 2 * q^18 + 2 * q^19 + 51 * q^20 + 4 * q^21 + 20 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 3 * q^26 + 3 * q^27 - 48 * q^28 - 10 * q^29 + 8 * q^30 + 8 * q^31 + 55 * q^32 - 8 * q^33 + 6 * q^34 + 31 * q^35 - 6 * q^36 + 20 * q^37 - 20 * q^38 - 10 * q^39 - 59 * q^40 - 68 * q^41 - 19 * q^42 - 3 * q^43 - 10 * q^44 + 14 * q^45 - 12 * q^46 + 19 * q^47 + 24 * q^48 + 17 * q^49 + 23 * q^50 + 11 * q^51 - 4 * q^52 - q^53 - 5 * q^54 + 3 * q^55 + 7 * q^56 - 2 * q^57 - 30 * q^58 + 20 * q^59 + 47 * q^60 + 24 * q^61 + 79 * q^62 + 3 * q^63 - 23 * q^64 + 6 * q^65 + 50 * q^66 - 14 * q^67 - 8 * q^68 - 8 * q^69 + 28 * q^70 - 28 * q^71 + 4 * q^72 + 43 * q^73 - 47 * q^74 - 18 * q^75 + 19 * q^76 + 26 * q^77 - 11 * q^78 + 9 * q^79 - 74 * q^80 - 3 * q^81 - 17 * q^82 + 8 * q^83 - 15 * q^84 - 21 * q^85 - 140 * q^86 - 11 * q^87 - 58 * q^88 - 6 * q^89 + 6 * q^90 - 15 * q^91 + 11 * q^92 - 8 * q^93 + 6 * q^94 - 16 * q^95 + 36 * q^96 - 81 * q^97 - 11 * q^98 - 6 * q^99

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