LMFDB - Embedded newform 87.2.g.b.25.2

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			25.2
Root			$0.824998 + 0.397298i$ of defining polynomial
Character	$\chi$	$=$	87.25
Dual form			87.2.g.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203758 - 0.892721i) q^{2} +(0.900969 - 0.433884i) q^{3} +(1.04650 + 0.503970i) q^{4} +(-0.0634200 + 0.277861i) q^{5} +(-0.203758 - 0.892721i) q^{6} +(-4.54015 + 2.18642i) q^{7} +(1.80497 - 2.26336i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})$	\(q+(0.203758 - 0.892721i) q^{2} +(0.900969 - 0.433884i) q^{3} +(1.04650 + 0.503970i) q^{4} +(-0.0634200 + 0.277861i) q^{5} +(-0.203758 - 0.892721i) q^{6} +(-4.54015 + 2.18642i) q^{7} +(1.80497 - 2.26336i) q^{8} +(0.623490 - 0.781831i) q^{9} +(0.235130 + 0.113233i) q^{10} +(-2.60766 - 3.26990i) q^{11} +1.16153 q^{12} +(1.41861 + 1.77888i) q^{13} +(1.02677 + 4.49858i) q^{14} +(0.0634200 + 0.277861i) q^{15} +(-0.204365 - 0.256265i) q^{16} -3.40834 q^{17} +(-0.570916 - 0.715906i) q^{18} +(-0.768127 - 0.369911i) q^{19} +(-0.206403 + 0.258821i) q^{20} +(-3.14188 + 3.93979i) q^{21} +(-3.45044 + 1.66164i) q^{22} +(1.61144 + 7.06017i) q^{23} +(0.644186 - 2.82237i) q^{24} +(4.43166 + 2.13417i) q^{25} +(1.87710 - 0.903962i) q^{26} +(0.222521 - 0.974928i) q^{27} -5.85318 q^{28} +(2.41553 - 4.81302i) q^{29} +0.260975 q^{30} +(0.728037 - 3.18974i) q^{31} +(4.94610 - 2.38192i) q^{32} +(-3.76817 - 1.81466i) q^{33} +(-0.694475 + 3.04269i) q^{34} +(-0.319585 - 1.40019i) q^{35} +(1.04650 - 0.503970i) q^{36} +(0.237365 - 0.297647i) q^{37} +(-0.486739 + 0.610351i) q^{38} +(2.04995 + 0.987204i) q^{39} +(0.514429 + 0.645074i) q^{40} -5.56008 q^{41} +(2.87695 + 3.60758i) q^{42} +(-1.75856 - 7.70474i) q^{43} +(-1.08099 - 4.73615i) q^{44} +(0.177699 + 0.222827i) q^{45} +6.63110 q^{46} +(4.07504 + 5.10993i) q^{47} +(-0.295316 - 0.142216i) q^{48} +(11.4681 - 14.3805i) q^{49} +(2.80821 - 3.52138i) q^{50} +(-3.07081 + 1.47882i) q^{51} +(0.588079 + 2.57654i) q^{52} +(-0.643658 + 2.82005i) q^{53} +(-0.824998 - 0.397298i) q^{54} +(1.07396 - 0.517190i) q^{55} +(-3.24617 + 14.2224i) q^{56} -0.852557 q^{57} +(-3.80450 - 3.13709i) q^{58} -4.68212 q^{59} +(-0.0736644 + 0.322745i) q^{60} +(6.25207 - 3.01084i) q^{61} +(-2.69920 - 1.29987i) q^{62} +(-1.12132 + 4.91284i) q^{63} +(-1.26445 - 5.53994i) q^{64} +(-0.584250 + 0.281360i) q^{65} +(-2.38778 + 2.99418i) q^{66} +(-1.77109 + 2.22087i) q^{67} +(-3.56684 - 1.71770i) q^{68} +(4.51515 + 5.66182i) q^{69} -1.31510 q^{70} +(-7.16657 - 8.98660i) q^{71} +(-0.644186 - 2.82237i) q^{72} +(2.51970 + 11.0395i) q^{73} +(-0.217350 - 0.272549i) q^{74} +4.91877 q^{75} +(-0.617425 - 0.774227i) q^{76} +(18.9885 + 9.14439i) q^{77} +(1.29899 - 1.62888i) q^{78} +(-4.22068 + 5.29256i) q^{79} +(0.0841670 - 0.0405327i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-1.13291 + 4.96360i) q^{82} +(-5.65795 - 2.72473i) q^{83} +(-5.27353 + 2.53960i) q^{84} +(0.216157 - 0.947045i) q^{85} -7.23650 q^{86} +(0.0880280 - 5.38445i) q^{87} -12.1077 q^{88} +(-1.26972 + 5.56302i) q^{89} +(0.235130 - 0.113233i) q^{90} +(-10.3301 - 4.97470i) q^{91} +(-1.87174 + 8.20062i) q^{92} +(-0.728037 - 3.18974i) q^{93} +(5.39206 - 2.59668i) q^{94} +(0.151498 - 0.189973i) q^{95} +(3.42281 - 4.29207i) q^{96} +(-0.453007 - 0.218157i) q^{97} +(-10.5011 - 13.1679i) q^{98} -4.18236 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 $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

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 $

$2$	0.203758	−	0.892721i	0.144078	−	0.631249i	−0.850385	−	0.526162i	$-0.823631\pi$
$2$	0.203758	−	0.892721i	0.144078	−	0.631249i	0.994463	−	0.105087i	$-0.0335122\pi$
$3$	0.900969	−	0.433884i	0.520175	−	0.250503i
$3$	0.900969	−	0.433884i	0.520175	−	0.250503i
$4$	1.04650	+	0.503970i	0.523252	+	0.251985i
$5$	−0.0634200	+	0.277861i	−0.0283623	+	0.124263i	−0.987127	−	0.159937i	$-0.948871\pi$
$5$	−0.0634200	+	0.277861i	−0.0283623	+	0.124263i	0.958765	+	0.284200i	$0.0917281\pi$
$6$	−0.203758	−	0.892721i	−0.0831837	−	0.364452i
$7$	−4.54015	+	2.18642i	−1.71601	+	0.826389i	−0.725624	+	0.688092i	$0.758449\pi$
$7$	−4.54015	+	2.18642i	−1.71601	+	0.826389i	−0.990391	+	0.138298i	$0.955837\pi$
$8$	1.80497	−	2.26336i	0.638153	−	0.800219i
$9$	0.623490	−	0.781831i	0.207830	−	0.260610i
$10$	0.235130	+	0.113233i	0.0743547	+	0.0358073i
$11$	−2.60766	−	3.26990i	−0.786238	−	0.985912i	−0.999959	−	0.00901707i	$-0.997130\pi$
$11$	−2.60766	−	3.26990i	−0.786238	−	0.985912i	0.213721	−	0.976895i	$-0.431442\pi$
$12$	1.16153			0.335306
$13$	1.41861	+	1.77888i	0.393452	+	0.493373i	0.938620	−	0.344954i	$-0.112106\pi$
$13$	1.41861	+	1.77888i	0.393452	+	0.493373i	−0.545168	+	0.838327i	$0.683534\pi$
$14$	1.02677	+	4.49858i	0.274416	+	1.20230i
$15$	0.0634200	+	0.277861i	0.0163750	+	0.0717435i
$16$	−0.204365	−	0.256265i	−0.0510912	−	0.0640663i
$17$	−3.40834			−0.826644			−0.413322	−	0.910585i	$-0.635632\pi$
$17$	−3.40834			−0.826644			−0.413322	+	0.910585i	$0.635632\pi$
$18$	−0.570916	−	0.715906i	−0.134566	−	0.168741i
$19$	−0.768127	−	0.369911i	−0.176221	−	0.0848633i	0.343694	−	0.939082i	$-0.388322\pi$
$19$	−0.768127	−	0.369911i	−0.176221	−	0.0848633i	−0.519914	+	0.854218i	$0.674036\pi$
$20$	−0.206403	+	0.258821i	−0.0461531	+	0.0578742i
$21$	−3.14188	+	3.93979i	−0.685614	+	0.859733i
$22$	−3.45044	+	1.66164i	−0.735636	+	0.354263i
$23$	1.61144	+	7.06017i	0.336008	+	1.47215i	0.807285	+	0.590162i	$0.200936\pi$
$23$	1.61144	+	7.06017i	0.336008	+	1.47215i	−0.471277	+	0.881985i	$0.656207\pi$
$24$	0.644186	−	2.82237i	0.131494	−	0.576113i
$25$	4.43166	+	2.13417i	0.886332	+	0.426835i
$26$	1.87710	−	0.903962i	0.368129	−	0.177281i
$27$	0.222521	−	0.974928i	0.0428242	−	0.187625i
$28$	−5.85318			−1.10615
$29$	2.41553	−	4.81302i	0.448553	−	0.893756i
$29$	2.41553	−	4.81302i	0.448553	−	0.893756i
$30$	0.260975			0.0476473
$31$	0.728037	−	3.18974i	0.130759	−	0.572894i	−0.866518	−	0.499146i	$-0.833647\pi$
$31$	0.728037	−	3.18974i	0.130759	−	0.572894i	0.997277	−	0.0737475i	$-0.0234959\pi$
$32$	4.94610	−	2.38192i	0.874355	−	0.421067i
$33$	−3.76817	−	1.81466i	−0.655955	−	0.315891i
$34$	−0.694475	+	3.04269i	−0.119101	+	0.521818i
$35$	−0.319585	−	1.40019i	−0.0540197	−	0.236676i
$36$	1.04650	−	0.503970i	0.174417	−	0.0839950i
$37$	0.237365	−	0.297647i	0.0390226	−	0.0489328i	−0.761937	−	0.647651i	$-0.775752\pi$
$37$	0.237365	−	0.297647i	0.0390226	−	0.0489328i	0.800960	+	0.598718i	$0.204323\pi$
$38$	−0.486739	+	0.610351i	−0.0789594	+	0.0990120i
$39$	2.04995	+	0.987204i	0.328255	+	0.158079i
$40$	0.514429	+	0.645074i	0.0813384	+	0.101995i
$41$	−5.56008			−0.868339			−0.434169	−	0.900831i	$-0.642958\pi$
$41$	−5.56008			−0.868339			−0.434169	+	0.900831i	$0.642958\pi$
$42$	2.87695	+	3.60758i	0.443923	+	0.556662i
$43$	−1.75856	−	7.70474i	−0.268177	−	1.17496i	−0.912131	−	0.409898i	$-0.865564\pi$
$43$	−1.75856	−	7.70474i	−0.268177	−	1.17496i	0.643954	−	0.765064i	$-0.277293\pi$
$44$	−1.08099	−	4.73615i	−0.162966	−	0.714001i
$45$	0.177699	+	0.222827i	0.0264898	+	0.0332172i
$46$	6.63110			0.977702
$47$	4.07504	+	5.10993i	0.594405	+	0.745360i	0.984494	−	0.175417i	$-0.0561273\pi$
$47$	4.07504	+	5.10993i	0.594405	+	0.745360i	−0.390089	+	0.920777i	$0.627556\pi$
$48$	−0.295316	−	0.142216i	−0.0426251	−	0.0205272i
$49$	11.4681	−	14.3805i	1.63830	−	2.05436i
$50$	2.80821	−	3.52138i	0.397140	−	0.497998i
$51$	−3.07081	+	1.47882i	−0.429999	+	0.207077i
$52$	0.588079	+	2.57654i	0.0815520	+	0.357302i
$53$	−0.643658	+	2.82005i	−0.0884132	+	0.387363i	−0.999702	−	0.0244039i	$-0.992231\pi$
$53$	−0.643658	+	2.82005i	−0.0884132	+	0.387363i	0.911289	+	0.411767i	$0.135088\pi$
$54$	−0.824998	−	0.397298i	−0.112268	−	0.0540654i
$55$	1.07396	−	0.517190i	0.144812	−	0.0697379i
$56$	−3.24617	+	14.2224i	−0.433788	+	1.90055i
$57$	−0.852557			−0.112924
$58$	−3.80450	−	3.13709i	−0.499556	−	0.411920i
$59$	−4.68212			−0.609560			−0.304780	−	0.952423i	$-0.598583\pi$
$59$	−4.68212			−0.609560			−0.304780	+	0.952423i	$0.598583\pi$
$60$	−0.0736644	+	0.322745i	−0.00951004	+	0.0416662i
$61$	6.25207	−	3.01084i	0.800495	−	0.385498i	0.0115280	−	0.999934i	$-0.496330\pi$
$61$	6.25207	−	3.01084i	0.800495	−	0.385498i	0.788967	+	0.614435i	$0.210616\pi$
$62$	−2.69920	−	1.29987i	−0.342799	−	0.165083i
$63$	−1.12132	+	4.91284i	−0.141274	+	0.618960i
$64$	−1.26445	−	5.53994i	−0.158057	−	0.692492i
$65$	−0.584250	+	0.281360i	−0.0724673	+	0.0348984i
$66$	−2.38778	+	2.99418i	−0.293915	+	0.368558i
$67$	−1.77109	+	2.22087i	−0.216373	+	0.271323i	−0.878158	−	0.478370i	$-0.841228\pi$
$67$	−1.77109	+	2.22087i	−0.216373	+	0.271323i	0.661785	+	0.749693i	$0.269799\pi$
$68$	−3.56684	−	1.71770i	−0.432543	−	0.208302i
$69$	4.51515	+	5.66182i	0.543560	+	0.681602i
$70$	−1.31510			−0.157184
$71$	−7.16657	−	8.98660i	−0.850516	−	1.06651i	−0.997008	−	0.0773013i	$-0.975370\pi$
$71$	−7.16657	−	8.98660i	−0.850516	−	1.06651i	0.146492	−	0.989212i	$-0.453202\pi$
$72$	−0.644186	−	2.82237i	−0.0759181	−	0.332619i
$73$	2.51970	+	11.0395i	0.294908	+	1.29208i	0.877603	+	0.479387i	$0.159141\pi$
$73$	2.51970	+	11.0395i	0.294908	+	1.29208i	−0.582695	+	0.812691i	$0.698002\pi$
$74$	−0.217350	−	0.272549i	−0.0252665	−	0.0316832i
$75$	4.91877			0.567971
$76$	−0.617425	−	0.774227i	−0.0708235	−	0.0888099i
$77$	18.9885	+	9.14439i	2.16394	+	1.04210i
$78$	1.29899	−	1.62888i	0.147082	−	0.184435i
$79$	−4.22068	+	5.29256i	−0.474863	+	0.595460i	−0.960354	−	0.278782i	$-0.910069\pi$
$79$	−4.22068	+	5.29256i	−0.474863	+	0.595460i	0.485491	+	0.874241i	$0.338641\pi$
$80$	0.0841670	−	0.0405327i	0.00941016	−	0.00453169i
$81$	−0.222521	−	0.974928i	−0.0247245	−	0.108325i
$82$	−1.13291	+	4.96360i	−0.125109	+	0.548138i
$83$	−5.65795	−	2.72473i	−0.621041	−	0.299078i	0.0967793	−	0.995306i	$-0.469146\pi$
$83$	−5.65795	−	2.72473i	−0.621041	−	0.299078i	−0.717821	+	0.696228i	$0.754860\pi$
$84$	−5.27353	+	2.53960i	−0.575389	+	0.277093i
$85$	0.216157	−	0.947045i	0.0234455	−	0.102721i
$86$	−7.23650			−0.780332
$87$	0.0880280	−	5.38445i	0.00943759	−	0.577273i
$88$	−12.1077			−1.29069
$89$	−1.26972	+	5.56302i	−0.134590	+	0.589679i	0.861981	+	0.506941i	$0.169224\pi$
$89$	−1.26972	+	5.56302i	−0.134590	+	0.589679i	−0.996571	+	0.0827384i	$0.973633\pi$
$90$	0.235130	−	0.113233i	0.0247849	−	0.0119358i
$91$	−10.3301	−	4.97470i	−1.08289	−	0.521491i
$92$	−1.87174	+	8.20062i	−0.195142	+	0.854974i
$93$	−0.728037	−	3.18974i	−0.0754939	−	0.330760i
$94$	5.39206	−	2.59668i	0.556149	−	0.267827i
$95$	0.151498	−	0.189973i	0.0155434	−	0.0194908i
$96$	3.42281	−	4.29207i	0.349339	−	0.438057i
$97$	−0.453007	−	0.218157i	−0.0459959	−	0.0221505i	0.410744	−	0.911751i	$-0.365269\pi$
$97$	−0.453007	−	0.218157i	−0.0459959	−	0.0221505i	−0.456740	+	0.889600i	$0.650983\pi$
$98$	−10.5011	−	13.1679i	−1.06077	−	1.33016i
$99$	−4.18236			−0.420343
$100$	3.56219	+	4.46685i	0.356219	+	0.446685i
$101$	1.00310	+	4.39485i	0.0998117	+	0.437304i	0.999998	+	0.00179942i	$0.000572775\pi$
$101$	1.00310	+	4.39485i	0.0998117	+	0.437304i	−0.900187	+	0.435504i	$0.856570\pi$
$102$	0.694475	+	3.04269i	0.0687633	+	0.301272i
$103$	5.06515	+	6.35150i	0.499085	+	0.625832i	0.966023	−	0.258458i	$-0.0832143\pi$
$103$	5.06515	+	6.35150i	0.499085	+	0.625832i	−0.466938	+	0.884290i	$0.654643\pi$
$104$	6.58680			0.645889
$105$	−0.895458	−	1.12287i	−0.0873877	−	0.109581i
$106$	2.38636	+	1.14921i	0.231784	+	0.111621i
$107$	5.93513	−	7.44241i	0.573770	−	0.719485i	−0.407266	−	0.913310i	$-0.633518\pi$
$107$	5.93513	−	7.44241i	0.573770	−	0.719485i	0.981036	+	0.193824i	$0.0620892\pi$
$108$	0.724204	−	0.908123i	0.0696866	−	0.0873842i
$109$	6.69547	−	3.22437i	0.641309	−	0.308838i	−0.0848202	−	0.996396i	$-0.527032\pi$
$109$	6.69547	−	3.22437i	0.641309	−	0.308838i	0.726129	+	0.687558i	$0.241317\pi$
$110$	−0.242879	−	1.06412i	−0.0231576	−	0.101460i
$111$	0.0847148	−	0.371160i	0.00804077	−	0.0352289i
$112$	1.48815	+	0.716655i	0.140617	+	0.0677175i
$113$	−3.81835	+	1.83882i	−0.359200	+	0.172981i	−0.604776	−	0.796396i	$-0.706737\pi$
$113$	−3.81835	+	1.83882i	−0.359200	+	0.172981i	0.245576	+	0.969377i	$0.421023\pi$
$114$	−0.173715	+	0.761095i	−0.0162699	+	0.0712831i
$115$	−2.06394			−0.192464
$116$	4.95349	−	3.81950i	0.459920	−	0.354631i
$117$	2.27527			0.210349
$118$	−0.954018	+	4.17983i	−0.0878245	+	0.384784i
$119$	15.4744	−	7.45206i	1.41853	−	0.683129i
$120$	0.743372	+	0.357989i	0.0678602	+	0.0326798i
$121$	−1.44463	+	6.32935i	−0.131330	+	0.575396i
$122$	−1.41393	−	6.19483i	−0.128011	−	0.560854i
$123$	−5.00946	+	2.41243i	−0.451688	+	0.217521i
$124$	2.36943	−	2.97117i	0.212781	−	0.266819i
$125$	−1.76256	+	2.21017i	−0.157648	+	0.197684i
$126$	4.15732	+	2.00206i	0.370363	+	0.178357i
$127$	−10.5989	−	13.2906i	−0.940501	−	1.17935i	−0.983615	−	0.180281i	$-0.942299\pi$
$127$	−10.5989	−	13.2906i	−0.940501	−	1.17935i	0.0431137	−	0.999070i	$-0.486272\pi$
$128$	5.77626			0.510554
$129$	−4.92737	−	6.17872i	−0.433831	−	0.544006i
$130$	0.132130	+	0.578901i	0.0115886	+	0.0507730i
$131$	2.82494	+	12.3769i	0.246816	+	1.08137i	0.934668	+	0.355521i	$0.115697\pi$
$131$	2.82494	+	12.3769i	0.246816	+	1.08137i	−0.687852	+	0.725851i	$0.741446\pi$
$132$	−3.02888	−	3.79810i	−0.263630	−	0.330582i
$133$	4.29619			0.372527
$134$	1.62175	+	2.03361i	0.140098	+	0.175677i
$135$	0.256782	+	0.123660i	0.0221003	+	0.0106429i
$136$	−6.15195	+	7.71430i	−0.527525	+	0.661496i
$137$	6.07484	−	7.61760i	0.519008	−	0.650816i	−0.451390	−	0.892327i	$-0.649072\pi$
$137$	6.07484	−	7.61760i	0.519008	−	0.650816i	0.970398	+	0.241511i	$0.0776430\pi$
$138$	5.97441	−	2.87713i	0.508576	−	0.244917i
$139$	2.77783	+	12.1705i	0.235612	+	1.03228i	0.944898	+	0.327364i	$0.106160\pi$
$139$	2.77783	+	12.1705i	0.235612	+	1.03228i	−0.709286	+	0.704921i	$0.750983\pi$
$140$	0.371209	−	1.62637i	0.0313729	−	0.137453i
$141$	5.88860	+	2.83580i	0.495909	+	0.238817i
$142$	−9.48277	+	4.56666i	−0.795776	+	0.383226i
$143$	2.11751	−	9.27742i	0.177075	−	0.775817i
$144$	−0.327776			−0.0273146
$145$	1.18416	+	0.976425i	0.0983391	+	0.0810877i
$146$	10.3686			0.858113
$147$	4.09291	−	17.9322i	0.337578	−	1.47902i
$148$	0.398409	−	0.191864i	0.0327490	−	0.0157711i
$149$	20.3625	+	9.80607i	1.66816	+	0.803345i	0.998137	+	0.0610063i	$0.0194310\pi$
$149$	20.3625	+	9.80607i	1.66816	+	0.803345i	0.670025	+	0.742338i	$0.266283\pi$
$150$	1.00224	−	4.39109i	0.0818323	−	0.358531i
$151$	1.47657	+	6.46927i	0.120161	+	0.526462i	0.998800	+	0.0489743i	$0.0155952\pi$
$151$	1.47657	+	6.46927i	0.120161	+	0.526462i	−0.878639	+	0.477487i	$0.841548\pi$
$152$	−2.22369	+	1.07087i	−0.180365	+	0.0868592i
$153$	−2.12506	+	2.66475i	−0.171801	+	0.215432i
$154$	12.0324	−	15.0882i	0.969602	−	1.21584i
$155$	0.840133	+	0.404587i	0.0674811	+	0.0324972i
$156$	1.64776	+	2.06623i	0.131927	+	0.165431i
$157$	−13.3793			−1.06778			−0.533890	−	0.845554i	$-0.679270\pi$
$157$	−13.3793			−1.06778			−0.533890	+	0.845554i	$0.679270\pi$
$158$	3.86478	+	4.84628i	0.307466	+	0.385550i
$159$	0.643658	+	2.82005i	0.0510454	+	0.223644i
$160$	0.348161	+	1.52539i	0.0275245	+	0.120593i
$161$	−22.7527	−	28.5309i	−1.79316	−	2.24855i
$162$	−0.915678			−0.0719425
$163$	6.33230	+	7.94046i	0.495984	+	0.621944i	0.965318	−	0.261076i	$-0.0840774\pi$
$163$	6.33230	+	7.94046i	0.495984	+	0.621944i	−0.469334	+	0.883021i	$0.655506\pi$
$164$	−5.81865	−	2.80212i	−0.454360	−	0.218808i
$165$	0.743201	−	0.931944i	0.0578581	−	0.0725518i
$166$	−3.58527	+	4.49579i	−0.278271	+	0.348941i
$167$	−22.1004	+	10.6430i	−1.71018	+	0.823579i	−0.718398	+	0.695632i	$0.755124\pi$
$167$	−22.1004	+	10.6430i	−1.71018	+	0.823579i	−0.991781	+	0.127947i	$0.959161\pi$
$168$	3.24617	+	14.2224i	0.250448	+	1.09728i
$169$	1.74081	−	7.62699i	0.133908	−	0.586691i
$170$	−0.801403	−	0.385935i	−0.0614648	−	0.0295999i
$171$	−0.768127	+	0.369911i	−0.0587402	+	0.0282878i
$172$	2.04262	−	8.94931i	0.155748	−	0.682379i
$173$	−22.0884			−1.67935			−0.839674	−	0.543091i	$-0.817254\pi$
$173$	−22.0884			−1.67935			−0.839674	+	0.543091i	$0.817254\pi$
$174$	−4.78887	−	1.17571i	−0.363043	−	0.0891301i
$175$	−24.7866			−1.87369
$176$	−0.305048	+	1.33650i	−0.0229939	+	0.100743i
$177$	−4.21845	+	2.03150i	−0.317078	+	0.152697i
$178$	4.70751	+	2.26702i	0.352843	+	0.169920i
$179$	−0.163565	+	0.716626i	−0.0122254	+	0.0535631i	−0.980673	−	0.195655i	$-0.937317\pi$
$179$	−0.163565	+	0.716626i	−0.0122254	+	0.0535631i	0.968447	+	0.249219i	$0.0801737\pi$
$180$	0.0736644	+	0.322745i	0.00549062	+	0.0240560i
$181$	−12.3221	+	5.93399i	−0.915892	+	0.441070i	−0.831603	−	0.555371i	$-0.812576\pi$
$181$	−12.3221	+	5.93399i	−0.915892	+	0.441070i	−0.0842890	+	0.996441i	$0.526862\pi$
$182$	−6.54585	+	8.20824i	−0.485211	+	0.608435i
$183$	4.32656	−	5.42534i	0.319829	−	0.401053i
$184$	18.8883	+	9.09613i	1.39246	+	0.670576i
$185$	0.0676508	+	0.0848314i	0.00497379	+	0.00623693i
$186$	−2.99589			−0.219669
$187$	8.88778	+	11.1449i	0.649939	+	0.814998i
$188$	1.68929	+	7.40127i	0.123204	+	0.539793i
$189$	1.12132	+	4.91284i	0.0815643	+	0.357357i
$190$	−0.138724	−	0.173954i	−0.0100641	−	0.0126200i
$191$	1.16101			0.0840075			0.0420038	−	0.999117i	$-0.486626\pi$
$191$	1.16101			0.0840075			0.0420038	+	0.999117i	$0.486626\pi$
$192$	−3.54292	−	4.44268i	−0.255688	−	0.320623i
$193$	−18.5608	−	8.93843i	−1.33604	−	0.643402i	−0.376878	−	0.926263i	$-0.623002\pi$
$193$	−18.5608	−	8.93843i	−1.33604	−	0.643402i	−0.959161	+	0.282861i	$0.908717\pi$
$194$	−0.287057	+	0.359958i	−0.0206095	+	0.0258434i
$195$	−0.404314	+	0.506993i	−0.0289535	+	0.0363065i
$196$	19.2488	−	9.26971i	1.37491	−	0.662122i
$197$	−1.14781	−	5.02887i	−0.0817778	−	0.358292i	0.917438	−	0.397878i	$-0.130253\pi$
$197$	−1.14781	−	5.02887i	−0.0817778	−	0.358292i	−0.999216	+	0.0395860i	$0.987396\pi$
$198$	−0.852187	+	3.73368i	−0.0605623	+	0.265341i
$199$	2.52796	+	1.21740i	0.179203	+	0.0862995i	0.521334	−	0.853353i	$-0.325435\pi$
$199$	2.52796	+	1.21740i	0.179203	+	0.0862995i	−0.342131	+	0.939652i	$0.611149\pi$
$200$	12.8294	−	6.17832i	0.907177	−	0.436874i
$201$	−0.632094	+	2.76938i	−0.0445845	+	0.195337i
$202$	4.12776			0.290428
$203$	−0.443589	+	27.1332i	−0.0311339	+	1.90438i
$204$	−3.95890			−0.277178
$205$	0.352620	−	1.54493i	0.0246281	−	0.107903i
$206$	6.70218	−	3.22760i	0.466963	−	0.224878i
$207$	6.52458	+	3.14207i	0.453489	+	0.218389i
$208$	0.165951	−	0.727081i	0.0115067	−	0.0504140i
$209$	0.793443	+	3.47630i	0.0548836	+	0.240461i
$210$	−1.18486	+	0.570600i	−0.0817634	+	0.0393752i
$211$	−3.02315	+	3.79091i	−0.208122	+	0.260977i	−0.874926	−	0.484256i	$-0.839090\pi$
$211$	−3.02315	+	3.79091i	−0.208122	+	0.260977i	0.666804	+	0.745233i	$0.267662\pi$
$212$	−2.09481	+	2.62681i	−0.143872	+	0.180410i
$213$	−10.3560	−	4.98719i	−0.709581	−	0.341716i
$214$	−5.43467	−	6.81486i	−0.371506	−	0.465854i
$215$	2.25238			0.153611
$216$	−1.80497	−	2.26336i	−0.122813	−	0.154002i
$217$	3.66871	+	16.0737i	0.249048	+	1.09115i
$218$	−1.51421	−	6.63417i	−0.102555	−	0.449323i
$219$	7.06004	+	8.85301i	0.477073	+	0.598231i
$220$	1.38455			0.0933463
$221$	−4.83510	−	6.06303i	−0.325244	−	0.407843i
$222$	−0.314081	−	0.151253i	−0.0210797	−	0.0101515i
$223$	6.48155	−	8.12761i	0.434037	−	0.544265i	−0.515924	−	0.856634i	$-0.672551\pi$
$223$	6.48155	−	8.12761i	0.434037	−	0.544265i	0.949961	+	0.312370i	$0.101123\pi$
$224$	−17.2482	+	21.6285i	−1.15244	+	1.44512i
$225$	4.43166	−	2.13417i	0.295444	−	0.142278i
$226$	0.863534	+	3.78339i	0.0574414	+	0.251667i
$227$	6.22713	−	27.2828i	0.413309	−	1.81083i	−0.154886	−	0.987932i	$-0.549501\pi$
$227$	6.22713	−	27.2828i	0.413309	−	1.81083i	0.568195	−	0.822894i	$-0.307642\pi$
$228$	−0.892205	−	0.429663i	−0.0590877	−	0.0284552i
$229$	3.14998	−	1.51695i	0.208156	−	0.100243i	−0.326901	−	0.945059i	$-0.606004\pi$
$229$	3.14998	−	1.51695i	0.208156	−	0.100243i	0.535057	+	0.844816i	$0.320290\pi$
$230$	−0.420544	+	1.84253i	−0.0277299	+	0.121493i
$231$	21.0757			1.38668
$232$	−6.53364	−	14.1546i	−0.428955	−	0.929294i
$233$	−3.35269			−0.219642			−0.109821	−	0.993951i	$-0.535028\pi$
$233$	−3.35269			−0.219642			−0.109821	+	0.993951i	$0.535028\pi$
$234$	0.463604	−	2.03118i	0.0303068	−	0.132783i
$235$	−1.67829	+	0.808222i	−0.109480	+	0.0527226i
$236$	−4.89986	−	2.35965i	−0.318954	−	0.153600i
$237$	−1.50634	+	6.59971i	−0.0978474	+	0.428698i
$238$	−3.49959	−	15.3327i	−0.226845	−	0.993871i
$239$	16.5718	−	7.98057i	1.07194	−	0.516220i	0.187210	−	0.982320i	$-0.440056\pi$
$239$	16.5718	−	7.98057i	1.07194	−	0.516220i	0.884732	+	0.466100i	$0.154341\pi$
$240$	0.0582454	−	0.0730374i	0.00375972	−	0.00471454i
$241$	3.50723	−	4.39793i	0.225921	−	0.283295i	−0.655933	−	0.754819i	$-0.727724\pi$
$241$	3.50723	−	4.39793i	0.225921	−	0.283295i	0.881853	+	0.471524i	$0.156296\pi$
$242$	5.35599	+	2.57931i	0.344296	+	0.165804i
$243$	−0.623490	−	0.781831i	−0.0399969	−	0.0501545i
$244$	8.06019			0.516001
$245$	3.26848	+	4.09855i	0.208816	+	0.261847i
$246$	1.13291	+	4.96360i	0.0722316	+	0.316468i
$247$	−0.431646	−	1.89117i	−0.0274650	−	0.120332i
$248$	−5.90545	−	7.40519i	−0.374996	−	0.470230i
$249$	−6.27986			−0.397970
$250$	1.61393	+	2.02381i	0.102074	+	0.127997i
$251$	24.1560	+	11.6329i	1.52472	+	0.734264i	0.993592	−	0.113030i	$-0.0360555\pi$
$251$	24.1560	+	11.6329i	1.52472	+	0.734264i	0.531124	+	0.847294i	$0.321770\pi$
$252$	−3.64940	+	4.57620i	−0.229890	+	0.288273i
$253$	18.8840	−	23.6797i	1.18722	−	1.48873i
$254$	−14.0244	+	6.75380i	−0.879970	+	0.423771i
$255$	−0.216157	−	0.947045i	−0.0135363	−	0.0593063i
$256$	3.70587	−	16.2365i	0.231617	−	1.01478i
$257$	3.33896	+	1.60796i	0.208279	+	0.100302i	0.535115	−	0.844779i	$-0.320268\pi$
$257$	3.33896	+	1.60796i	0.208279	+	0.100302i	−0.326836	+	0.945081i	$0.605983\pi$
$258$	−6.51986	+	3.13980i	−0.405909	+	0.195475i
$259$	−0.426893	+	1.87034i	−0.0265259	+	0.116217i
$260$	−0.753218			−0.0467126
$261$	−2.25691	−	4.88941i	−0.139699	−	0.302647i
$262$	11.6247			0.718176
$263$	−3.92794	+	17.2094i	−0.242207	+	1.06118i	0.696796	+	0.717270i	$0.254608\pi$
$263$	−3.92794	+	17.2094i	−0.242207	+	1.06118i	−0.939003	+	0.343910i	$0.888249\pi$
$264$	−10.9087	+	5.25334i	−0.671382	+	0.323321i
$265$	−0.742761	−	0.357695i	−0.0456275	−	0.0219730i
$266$	0.875382	−	3.83530i	0.0536731	−	0.235157i
$267$	1.26972	+	5.56302i	0.0777058	+	0.340451i
$268$	−2.97271	+	1.43158i	−0.181587	+	0.0874477i
$269$	−8.93835	+	11.2083i	−0.544981	+	0.683385i	−0.975702	−	0.219100i	$-0.929688\pi$
$269$	−8.93835	+	11.2083i	−0.544981	+	0.683385i	0.430721	+	0.902485i	$0.358259\pi$
$270$	0.162715	−	0.204038i	0.00990253	−	0.0124174i
$271$	−27.2004	−	13.0990i	−1.65231	−	0.795709i	−0.999263	−	0.0383890i	$-0.987777\pi$
$271$	−27.2004	−	13.0990i	−1.65231	−	0.795709i	−0.653044	−	0.757320i	$-0.726508\pi$
$272$	0.696544	+	0.873439i	0.0422342	+	0.0529600i
$273$	−11.4655			−0.693925
$274$	−5.56260	−	6.97528i	−0.336049	−	0.421392i
$275$	−4.57771	−	20.0563i	−0.276047	−	1.20944i
$276$	1.87174	+	8.20062i	0.112665	+	0.493619i
$277$	5.26579	+	6.60309i	0.316391	+	0.396741i	0.914442	−	0.404716i	$-0.132630\pi$
$277$	5.26579	+	6.60309i	0.316391	+	0.396741i	−0.598052	+	0.801457i	$0.704058\pi$
$278$	11.4308			0.685575
$279$	−2.03991	−	2.55797i	−0.122126	−	0.153142i
$280$	−3.74599	−	1.80397i	−0.223866	−	0.107808i
$281$	−7.90311	+	9.91018i	−0.471460	+	0.591192i	−0.959528	−	0.281614i	$-0.909130\pi$
$281$	−7.90311	+	9.91018i	−0.471460	+	0.591192i	0.488068	+	0.872806i	$0.337702\pi$
$282$	3.73142	−	4.67906i	0.222203	−	0.278634i
$283$	22.2025	−	10.6921i	1.31980	−	0.635582i	0.364495	−	0.931205i	$-0.381242\pi$
$283$	22.2025	−	10.6921i	1.31980	−	0.635582i	0.955305	+	0.295623i	$0.0955273\pi$
$284$	−2.97088	−	13.0163i	−0.176289	−	0.772373i
$285$	0.0540692	−	0.236893i	0.00320278	−	0.0140323i
$286$	−7.85069	−	3.78069i	−0.464221	−	0.223557i
$287$	25.2436	−	12.1567i	1.49008	−	0.717586i
$288$	1.22159	−	5.35212i	0.0719827	−	0.315377i
$289$	−5.38323			−0.316661
$290$	1.11296	−	0.858169i	0.0653551	−	0.0503934i
$291$	−0.502800			−0.0294746
$292$	−2.92671	+	12.8228i	−0.171273	+	0.750396i
$293$	4.15097	−	1.99900i	0.242502	−	0.116783i	−0.308686	−	0.951164i	$-0.599889\pi$
$293$	4.15097	−	1.99900i	0.242502	−	0.116783i	0.551188	+	0.834381i	$0.314175\pi$
$294$	−15.1745	−	7.30765i	−0.884995	−	0.426191i
$295$	0.296940	−	1.30098i	0.0172885	−	0.0757460i
$296$	−0.245245	−	1.07449i	−0.0142546	−	0.0624533i
$297$	−3.76817	+	1.81466i	−0.218652	+	0.105297i
$298$	12.9031	−	16.1800i	0.747457	−	0.937281i
$299$	−10.2732	+	12.8822i	−0.594114	+	0.744996i
$300$	5.14752	+	2.47891i	0.297192	+	0.143120i
$301$	24.8299	+	31.1357i	1.43117	+	1.79463i
$302$	6.07611			0.349641
$303$	2.81061	+	3.52439i	0.161465	+	0.202471i
$304$	0.0621829	+	0.272441i	0.00356643	+	0.0156256i
$305$	0.440089	+	1.92815i	0.0251994	+	0.110406i
$306$	1.94588	+	2.44005i	0.111238	+	0.139488i
$307$	2.80588			0.160140			0.0800700	−	0.996789i	$-0.474486\pi$
$307$	2.80588			0.160140			0.0800700	+	0.996789i	$0.474486\pi$
$308$	15.2631	+	19.1393i	0.869695	+	1.09056i
$309$	7.31936	+	3.52482i	0.416384	+	0.200520i
$310$	0.532366	−	0.667566i	0.0302364	−	0.0379152i
$311$	9.80146	−	12.2906i	0.555790	−	0.696939i	−0.421983	−	0.906604i	$-0.638666\pi$
$311$	9.80146	−	12.2906i	0.555790	−	0.696939i	0.977773	+	0.209665i	$0.0672373\pi$
$312$	5.93450	−	2.85790i	0.335975	−	0.161797i
$313$	−4.05540	−	17.7679i	−0.229225	−	1.00430i	−0.950274	−	0.311415i	$-0.899197\pi$
$313$	−4.05540	−	17.7679i	−0.229225	−	1.00430i	0.721049	−	0.692884i	$-0.243660\pi$
$314$	−2.72612	+	11.9439i	−0.153844	+	0.674035i
$315$	−1.29397	−	0.623145i	−0.0729072	−	0.0351102i
$316$	−7.08425	+	3.41160i	−0.398520	+	0.191917i
$317$	−0.418332	+	1.83283i	−0.0234959	+	0.102942i	−0.985316	−	0.170740i	$-0.945384\pi$
$317$	−0.418332	+	1.83283i	−0.0234959	+	0.102942i	0.961820	+	0.273682i	$0.0882415\pi$
$318$	2.64866			0.148530
$319$	−22.0370	+	4.65217i	−1.23383	+	0.260471i
$320$	1.61952			0.0905342
$321$	2.11822	−	9.28054i	0.118228	−	0.517989i
$322$	−30.1062	+	14.4984i	−1.67775	+	0.807963i
$323$	2.61804	+	1.26078i	0.145672	+	0.0701517i
$324$	0.258465	−	1.13241i	0.0143592	−	0.0629117i
$325$	2.49035	+	10.9110i	0.138140	+	0.605231i
$326$	8.37886	−	4.03505i	0.464062	−	0.223481i
$327$	4.63341	−	5.81011i	0.256228	−	0.321300i
$328$	−10.0358	+	12.5845i	−0.554133	+	0.694861i
$329$	−29.6737	−	14.2901i	−1.63597	−	0.787839i
$330$	−0.680533	−	0.853361i	−0.0374621	−	0.0469760i
$331$	6.14086			0.337532			0.168766	−	0.985656i	$-0.446022\pi$
$331$	6.14086			0.337532			0.168766	+	0.985656i	$0.446022\pi$
$332$	−4.54790	−	5.70288i	−0.249598	−	0.312986i
$333$	−0.0847148	−	0.371160i	−0.00464234	−	0.0203394i
$334$	4.99809	+	21.8981i	0.273483	+	1.19821i
$335$	−0.504772	−	0.632965i	−0.0275787	−	0.0345825i
$336$	1.65172			0.0901088
$337$	−4.52153	−	5.66982i	−0.246304	−	0.308855i	0.643277	−	0.765634i	$-0.277575\pi$
$337$	−4.52153	−	5.66982i	−0.246304	−	0.308855i	−0.889580	+	0.456779i	$0.849003\pi$
$338$	−6.45407	−	3.10811i	−0.351055	−	0.169059i
$339$	−2.64238	+	3.31344i	−0.143514	+	0.179961i
$340$	0.703492	−	0.882151i	0.0381522	−	0.0478413i
$341$	−12.3286	+	5.93714i	−0.667631	+	0.321514i
$342$	0.173715	+	0.761095i	0.00939343	+	0.0411553i
$343$	−12.7757	+	55.9738i	−0.689821	+	3.02230i
$344$	−20.6128	−	9.92658i	−1.11137	−	0.535205i
$345$	−1.85955	+	0.895512i	−0.100115	+	0.0482127i
$346$	−4.50068	+	19.7187i	−0.241958	+	1.06009i
$347$	−1.50956			−0.0810374			−0.0405187	−	0.999179i	$-0.512901\pi$
$347$	−1.50956			−0.0810374			−0.0405187	+	0.999179i	$0.512901\pi$
$348$	2.80572	−	5.59049i	0.150402	−	0.299681i
$349$	14.5718			0.780011			0.390006	−	0.920813i	$-0.372473\pi$
$349$	14.5718			0.780011			0.390006	+	0.920813i	$0.372473\pi$
$350$	−5.05046	+	22.1275i	−0.269958	+	1.18276i
$351$	2.04995	−	0.987204i	0.109418	−	0.0526931i
$352$	−20.6864	−	9.96203i	−1.10259	−	0.530978i
$353$	4.85202	−	21.2581i	0.258247	−	1.13145i	−0.664877	−	0.746953i	$-0.731516\pi$
$353$	4.85202	−	21.2581i	0.258247	−	1.13145i	0.923124	−	0.384501i	$-0.125627\pi$
$354$	0.954018	+	4.17983i	0.0507055	+	0.222155i
$355$	2.95153	−	1.42138i	0.156651	−	0.0754392i
$356$	−4.13237	+	5.18183i	−0.219015	+	0.274636i
$357$	10.7086	−	13.4281i	0.566759	−	0.710693i
$358$	0.606419	+	0.292036i	0.0320502	+	0.0154346i
$359$	5.27111	+	6.60976i	0.278198	+	0.348850i	0.901225	−	0.433351i	$-0.142669\pi$
$359$	5.27111	+	6.60976i	0.278198	+	0.348850i	−0.623027	+	0.782200i	$0.714097\pi$
$360$	0.825080			0.0434855
$361$	−11.3931	−	14.2865i	−0.599638	−	0.751922i
$362$	2.78668	+	12.2093i	0.146465	+	0.641704i
$363$	1.44463	+	6.32935i	0.0758236	+	0.332205i
$364$	−8.30338	−	10.4121i	−0.435215	−	0.545743i
$365$	−3.22725			−0.168922
$366$	−3.96174	−	4.96787i	−0.207084	−	0.259675i
$367$	6.20750	+	2.98937i	0.324029	+	0.156044i	0.588825	−	0.808260i	$-0.299591\pi$
$367$	6.20750	+	2.98937i	0.324029	+	0.156044i	−0.264797	+	0.964304i	$0.585305\pi$
$368$	1.47995	−	1.85580i	0.0771480	−	0.0967405i
$369$	−3.46665	+	4.34705i	−0.180467	+	0.226298i
$370$	0.0895151	−	0.0431082i	0.00465367	−	0.00224109i
$371$	−3.24351	−	14.2107i	−0.168395	−	0.737785i
$372$	0.845639	−	3.70499i	0.0438443	−	0.192095i
$373$	17.3533	+	8.35690i	0.898519	+	0.432704i	0.825354	−	0.564616i	$-0.190976\pi$
$373$	17.3533	+	8.35690i	0.898519	+	0.432704i	0.0731653	+	0.997320i	$0.476690\pi$
$374$	11.7603	−	5.66344i	0.608108	−	0.292850i
$375$	−0.629049	+	2.75604i	−0.0324839	+	0.142321i
$376$	18.9209			0.975773
$377$	11.9885	−	2.53086i	0.617439	−	0.130346i
$378$	4.61427			0.237333
$379$	7.78248	−	34.0973i	0.399759	−	1.75146i	−0.228585	−	0.973524i	$-0.573410\pi$
$379$	7.78248	−	34.0973i	0.399759	−	1.75146i	0.628344	−	0.777936i	$-0.283733\pi$
$380$	0.254285	−	0.122457i	0.0130445	−	0.00628192i
$381$	−15.3159	−	7.37574i	−0.784656	−	0.377870i
$382$	0.236564	−	1.03645i	0.0121037	−	0.0530296i
$383$	4.55743	+	19.9674i	0.232874	+	1.02029i	0.947243	+	0.320517i	$0.103857\pi$
$383$	4.55743	+	19.9674i	0.232874	+	1.02029i	−0.714369	+	0.699769i	$0.753286\pi$
$384$	5.20423	−	2.50623i	0.265577	−	0.127895i
$385$	−3.74512	+	4.69624i	−0.190869	+	0.239342i
$386$	−11.7614	+	14.7484i	−0.598641	+	0.750672i
$387$	−7.12025	−	3.42893i	−0.361943	−	0.174302i
$388$	−0.364130	−	0.456604i	−0.0184859	−	0.0231806i
$389$	−7.13745			−0.361883			−0.180942	−	0.983494i	$-0.557914\pi$
$389$	−7.13745			−0.361883			−0.180942	+	0.983494i	$0.557914\pi$
$390$	0.370221	+	0.464243i	0.0187469	+	0.0235079i
$391$	−5.49232	−	24.0634i	−0.277759	−	1.21694i
$392$	−11.8488	−	51.9128i	−0.598453	−	2.62199i
$393$	7.91531	+	9.92548i	0.399274	+	0.500674i
$394$	−4.72325			−0.237954
$395$	−1.20292	−	1.50842i	−0.0605256	−	0.0758967i
$396$	−4.37686	−	2.10778i	−0.219945	−	0.105920i
$397$	−16.4091	+	20.5763i	−0.823548	+	1.03270i	0.175290	+	0.984517i	$0.443914\pi$
$397$	−16.4091	+	20.5763i	−0.823548	+	1.03270i	−0.998839	+	0.0481802i	$0.984658\pi$
$398$	1.60189	−	2.00871i	0.0802957	−	0.100688i
$399$	3.87074	−	1.86405i	0.193779	−	0.0933191i
$400$	−0.358760	−	1.57183i	−0.0179380	−	0.0785915i
$401$	1.12506	−	4.92921i	0.0561828	−	0.246153i	−0.939037	−	0.343817i	$-0.888280\pi$
$401$	1.12506	−	4.92921i	0.0561828	−	0.246153i	0.995219	+	0.0976641i	$0.0311371\pi$
$402$	2.34349	+	1.12857i	0.116883	+	0.0562878i
$403$	6.70696	−	3.22990i	0.334098	−	0.160893i
$404$	−1.16513	+	5.10476i	−0.0579673	+	0.253971i
$405$	0.285007			0.0141621
$406$	24.1320	+	5.92460i	1.19765	+	0.294033i
$407$	−1.59224			−0.0789246
$408$	−2.19561	+	9.61958i	−0.108699	+	0.476240i
$409$	−5.81490	+	2.80031i	−0.287529	+	0.138466i	−0.572089	−	0.820192i	$-0.693867\pi$
$409$	−5.81490	+	2.80031i	−0.287529	+	0.138466i	0.284560	+	0.958658i	$0.408152\pi$
$410$	−1.30734	−	0.629583i	−0.0645651	−	0.0310929i
$411$	2.16808	−	9.49900i	0.106944	−	0.468551i
$412$	2.09974	+	9.19957i	0.103447	+	0.453230i
$413$	21.2575	−	10.2371i	1.04601	−	0.503734i
$414$	4.13442	−	5.18440i	0.203196	−	0.254799i
$415$	1.11592	−	1.39932i	0.0547785	−	0.0686901i
$416$	11.2537	+	5.41951i	0.551760	+	0.265713i
$417$	7.78330	+	9.75995i	0.381150	+	0.477947i
$418$	3.26503			0.159698
$419$	0.767911	+	0.962930i	0.0375149	+	0.0470422i	0.800235	−	0.599686i	$-0.204708\pi$
$419$	0.767911	+	0.962930i	0.0375149	+	0.0470422i	−0.762720	+	0.646729i	$0.776137\pi$
$420$	−0.371209	−	1.62637i	−0.0181131	−	0.0793588i
$421$	−1.96888	−	8.62624i	−0.0959574	−	0.420417i	0.904018	−	0.427495i	$-0.140604\pi$
$421$	−1.96888	−	8.62624i	−0.0959574	−	0.420417i	−0.999975	+	0.00707841i	$0.997747\pi$
$422$	2.76823	+	3.47125i	0.134755	+	0.168978i
$423$	6.53585			0.317784
$424$	5.22100	+	6.54693i	0.253554	+	0.317947i
$425$	−15.1046	−	7.27399i	−0.732681	−	0.352840i
$426$	−6.56228	+	8.22884i	−0.317943	+	0.398688i
$427$	−21.8024	+	27.3393i	−1.05509	+	1.32304i
$428$	9.96189	−	4.79739i	0.481526	−	0.231891i
$429$	−2.11751	−	9.27742i	−0.102234	−	0.447918i
$430$	0.458939	−	2.01074i	0.0221320	−	0.0969667i
$431$	8.89025	+	4.28132i	0.428228	+	0.206224i	0.635568	−	0.772045i	$-0.280766\pi$
$431$	8.89025	+	4.28132i	0.428228	+	0.206224i	−0.207339	+	0.978269i	$0.566480\pi$
$432$	−0.295316	+	0.142216i	−0.0142084	+	0.00684239i
$433$	7.36319	−	32.2602i	0.353852	−	1.55033i	−0.414348	−	0.910119i	$-0.635990\pi$
$433$	7.36319	−	32.2602i	0.353852	−	1.55033i	0.768200	−	0.640210i	$-0.221153\pi$
$434$	15.0968			0.724671
$435$	1.49055	+	0.365941i	0.0714662	+	0.0175455i
$436$	8.63182			0.413389
$437$	1.37384	−	6.01920i	0.0657198	−	0.287937i
$438$	9.34180	−	4.49877i	0.446368	−	0.214960i
$439$	9.70775	+	4.67500i	0.463326	+	0.223126i	0.650958	−	0.759113i	$-0.274367\pi$
$439$	9.70775	+	4.67500i	0.463326	+	0.223126i	−0.187633	+	0.982239i	$0.560082\pi$
$440$	0.767871	−	3.36426i	0.0366068	−	0.160385i
$441$	−4.09291	−	17.9322i	−0.194901	−	0.853915i
$442$	−6.39778	+	3.08101i	−0.304311	+	0.146549i
$443$	21.2232	−	26.6130i	1.00834	−	1.26442i	0.0442056	−	0.999022i	$-0.485924\pi$
$443$	21.2232	−	26.6130i	1.00834	−	1.26442i	0.964138	−	0.265401i	$-0.0855042\pi$
$444$	0.275708	−	0.345727i	0.0130845	−	0.0164075i
$445$	−1.46522	−	0.705614i	−0.0694582	−	0.0334493i
$446$	−5.93502	−	7.44227i	−0.281031	−	0.352402i
$447$	22.6007			1.06898
$448$	17.8534	+	22.3875i	0.843495	+	1.05771i
$449$	4.86933	+	21.3339i	0.229798	+	1.00681i	0.949805	+	0.312843i	$0.101282\pi$
$449$	4.86933	+	21.3339i	0.229798	+	1.00681i	−0.720007	+	0.693967i	$0.755861\pi$
$450$	−1.00224	−	4.39109i	−0.0472459	−	0.206998i
$451$	14.4988	+	18.1809i	0.682721	+	0.856106i
$452$	−4.92263			−0.231541
$453$	4.13725	+	5.18795i	0.194385	+	0.243751i
$454$	−23.0871	−	11.1182i	−1.08353	−	0.521802i
$455$	2.03741	−	2.55483i	0.0955153	−	0.119772i
$456$	−1.53884	+	1.92964i	−0.0720628	+	0.0903639i
$457$	−26.2149	+	12.6244i	−1.22628	+	0.590546i	−0.931054	−	0.364881i	$-0.881110\pi$
$457$	−26.2149	+	12.6244i	−1.22628	+	0.590546i	−0.295227	+	0.955427i	$0.595395\pi$
$458$	−0.712379	−	3.12114i	−0.0332873	−	0.145841i
$459$	−0.758427	+	3.32288i	−0.0354003	+	0.155099i
$460$	−2.15993	−	1.04017i	−0.100707	−	0.0484980i
$461$	−16.8951	+	8.13623i	−0.786882	+	0.378942i	−0.783769	−	0.621053i	$-0.786705\pi$
$461$	−16.8951	+	8.13623i	−0.786882	+	0.378942i	−0.00311295	+	0.999995i	$0.500991\pi$
$462$	4.29433	−	18.8147i	0.199790	−	0.875338i
$463$	22.8658			1.06266			0.531332	−	0.847164i	$-0.321692\pi$
$463$	22.8658			1.06266			0.531332	+	0.847164i	$0.321692\pi$
$464$	−1.72706	+	0.364595i	−0.0801768	+	0.0169259i
$465$	0.932477			0.0432426
$466$	−0.683136	+	2.99301i	−0.0316456	+	0.138649i
$467$	−17.6886	+	8.51838i	−0.818530	+	0.394183i	−0.795801	−	0.605558i	$-0.792950\pi$
$467$	−17.6886	+	8.51838i	−0.818530	+	0.394183i	−0.0227293	+	0.999742i	$0.507236\pi$
$468$	2.38109	+	1.14667i	0.110066	+	0.0530048i
$469$	3.18524	−	13.9554i	0.147081	−	0.644402i
$470$	0.379552	+	1.66293i	0.0175074	+	0.0767051i
$471$	−12.0543	+	5.80504i	−0.555432	+	0.267482i
$472$	−8.45109	+	10.5973i	−0.388993	+	0.487782i
$473$	−20.6080	+	25.8416i	−0.947558	+	1.18820i
$474$	5.58477	+	2.68948i	0.256517	+	0.123532i
$475$	−2.61463	−	3.27864i	−0.119967	−	0.150434i
$476$	19.9496			0.914389
$477$	1.80349	+	2.26150i	0.0825761	+	0.103547i
$478$	−3.74778	−	16.4201i	−0.171420	−	0.751038i
$479$	−5.01171	−	21.9577i	−0.228991	−	1.00327i	−0.950465	−	0.310833i	$-0.899392\pi$
$479$	−5.01171	−	21.9577i	−0.228991	−	1.00327i	0.721474	−	0.692442i	$-0.243465\pi$
$480$	0.975524	+	1.22327i	0.0445264	+	0.0558343i
$481$	0.866207			0.0394957
$482$	−3.21150	−	4.02709i	−0.146280	−	0.183429i
$483$	−32.8785	−	15.8335i	−1.49603	−	0.720448i
$484$	−4.70162	+	5.89565i	−0.213710	+	0.267984i
$485$	0.0893470	−	0.112038i	0.00405704	−	0.00508737i
$486$	−0.824998	+	0.397298i	−0.0374227	+	0.0180218i
$487$	−0.382806	−	1.67718i	−0.0173466	−	0.0760003i	0.965514	−	0.260352i	$-0.0838386\pi$
$487$	−0.382806	−	1.67718i	−0.0173466	−	0.0760003i	−0.982860	+	0.184352i	$0.940981\pi$
$488$	4.47018	−	19.5852i	0.202356	−	0.886578i
$489$	9.15044	+	4.40662i	0.413797	+	0.199274i
$490$	4.32484	−	2.08273i	0.195376	−	0.0940882i
$491$	−6.55025	+	28.6985i	−0.295609	+	1.29515i	0.580985	+	0.813914i	$0.302668\pi$
$491$	−6.55025	+	28.6985i	−0.295609	+	1.29515i	−0.876593	+	0.481232i	$0.840190\pi$
$492$	−6.45822			−0.291159
$493$	−8.23296	+	16.4044i	−0.370794	+	0.738818i
$494$	−1.77623			−0.0799165
$495$	0.265245	−	1.16212i	0.0119219	−	0.0522332i
$496$	−0.966204	+	0.465299i	−0.0433838	+	0.0208926i
$497$	52.1858	+	25.1313i	2.34085	+	1.12730i
$498$	−1.27957	+	5.60616i	−0.0573388	+	0.251218i
$499$	3.09035	+	13.5397i	0.138343	+	0.606121i	0.995799	+	0.0915640i	$0.0291866\pi$
$499$	3.09035	+	13.5397i	0.138343	+	0.606121i	−0.857456	+	0.514557i	$0.827956\pi$
$500$	−2.95838	+	1.42468i	−0.132303	+	0.0637138i
$501$	−15.2939	+	19.1780i	−0.683283	+	0.856810i
$502$	15.3069	−	19.1943i	0.683182	−	0.856683i
$503$	23.8857	+	11.5027i	1.06501	+	0.512881i	0.882495	−	0.470322i	$-0.155862\pi$
$503$	23.8857	+	11.5027i	1.06501	+	0.512881i	0.182514	+	0.983203i	$0.441576\pi$
$504$	9.09558	+	11.4055i	0.405149	+	0.508041i
$505$	−1.28477			−0.0571717
$506$	−17.2916	−	21.6830i	−0.768707	−	0.963928i
$507$	−1.74081	−	7.62699i	−0.0773121	−	0.338726i
$508$	−4.39374	−	19.2502i	−0.194941	−	0.854091i
$509$	−3.59869	−	4.51261i	−0.159509	−	0.200018i	0.695654	−	0.718377i	$-0.255115\pi$
$509$	−3.59869	−	4.51261i	−0.159509	−	0.200018i	−0.855163	+	0.518359i	$0.826543\pi$
$510$	−0.889490			−0.0393873
$511$	−35.5768	−	44.6119i	−1.57383	−	1.97352i
$512$	−3.33106	−	1.60415i	−0.147213	−	0.0708942i
$513$	−0.531561	+	0.666556i	−0.0234690	+	0.0294292i
$514$	2.11580	−	2.65313i	0.0933239	−	0.117024i
$515$	−2.08607	+	1.00460i	−0.0919232	+	0.0442679i
$516$	−2.04262	−	8.94931i	−0.0899214	−	0.393972i
$517$	6.08267	−	26.6499i	0.267515	−	1.17206i
$518$	1.58271	+	0.762193i	0.0695403	+	0.0334888i
$519$	−19.9009	+	9.58379i	−0.873554	+	0.420682i
$520$	−0.417735	+	1.83022i	−0.0183189	+	0.0802603i
$521$	23.7796			1.04180			0.520901	−	0.853617i	$-0.325596\pi$
$521$	23.7796			1.04180			0.520901	+	0.853617i	$0.325596\pi$
$522$	−4.82474	+	1.01854i	−0.211173	+	0.0445802i
$523$	24.9044			1.08899			0.544497	−	0.838763i	$-0.316720\pi$
$523$	24.9044			1.08899			0.544497	+	0.838763i	$0.316720\pi$
$524$	−3.28126	+	14.3761i	−0.143343	+	0.628025i
$525$	−22.3319	+	10.7545i	−0.974646	+	0.469365i
$526$	14.5629	+	7.01311i	0.634971	+	0.305786i
$527$	−2.48140	+	10.8717i	−0.108091	+	0.473579i
$528$	0.305048	+	1.33650i	0.0132755	+	0.0581639i
$529$	−26.5270	+	12.7747i	−1.15335	+	0.555422i
$530$	−0.470665	+	0.590195i	−0.0204444	+	0.0256364i
$531$	−2.91925	+	3.66063i	−0.126685	+	0.158858i
$532$	4.49599	+	2.16515i	0.194926	+	0.0938713i
$533$	−7.88759	−	9.89072i	−0.341649	−	0.428415i
$534$	5.22494			0.226105
$535$	1.69155	+	2.12114i	0.0731322	+	0.0917048i
$536$	1.82988	+	8.01722i	0.0790387	+	0.346291i
$537$	0.163565	+	0.716626i	0.00705836	+	0.0309247i
$538$	8.18466	+	10.2632i	0.352866	+	0.442480i
$539$	−76.9277			−3.31351
$540$	0.206403	+	0.258821i	0.00888218	+	0.0111379i
$541$	18.8102	+	9.05851i	0.808713	+	0.389456i	0.792089	−	0.610406i	$-0.208994\pi$
$541$	18.8102	+	9.05851i	0.808713	+	0.389456i	0.0166244	+	0.999862i	$0.494708\pi$
$542$	−17.2361	+	21.6133i	−0.740352	+	0.928372i
$543$	−8.52713	+	10.6927i	−0.365934	+	0.458867i
$544$	−16.8580	+	8.11838i	−0.722780	+	0.348073i
$545$	0.471300	+	2.06490i	0.0201883	+	0.0884506i
$546$	−2.33619	+	10.2355i	−0.0999796	+	0.438039i
$547$	−0.170736	−	0.0822219i	−0.00730012	−	0.00351555i	0.430230	−	0.902719i	$-0.358432\pi$
$547$	−0.170736	−	0.0822219i	−0.00730012	−	0.00351555i	−0.437530	+	0.899204i	$0.644147\pi$
$548$	10.1964	−	4.91032i	0.435568	−	0.209759i
$549$	1.54413	−	6.76529i	0.0659020	−	0.288735i
$550$	−18.8374			−0.803229
$551$	−3.63583	+	2.80348i	−0.154891	+	0.119432i
$552$	20.9644			0.892306
$553$	7.59073	−	33.2572i	0.322791	−	1.41424i
$554$	6.96766	−	3.35545i	0.296027	−	0.142559i
$555$	0.0977583	+	0.0470779i	0.00414961	+	0.00199835i
$556$	−3.22654	+	14.1364i	−0.136836	+	0.599516i
$557$	5.48081	+	24.0130i	0.232229	+	1.01746i	0.947786	+	0.318908i	$0.103316\pi$
$557$	5.48081	+	24.0130i	0.232229	+	1.01746i	−0.715556	+	0.698555i	$0.753827\pi$
$558$	−2.69920	+	1.29987i	−0.114266	+	0.0550278i
$559$	11.2111	−	14.0583i	0.474179	−	0.594602i
$560$	−0.293509	+	0.368049i	−0.0124030	+	0.0155529i
$561$	12.8432	+	6.18497i	0.542241	+	0.261129i
$562$	7.23671	+	9.07454i	0.305262	+	0.382786i
$563$	−24.8717			−1.04822			−0.524109	−	0.851651i	$-0.675602\pi$
$563$	−24.8717			−1.04822			−0.524109	+	0.851651i	$0.675602\pi$
$564$	4.73329	+	5.93535i	0.199307	+	0.249924i
$565$	−0.268777	−	1.17759i	−0.0113075	−	0.0495415i
$566$	−5.02117	−	21.9992i	−0.211056	−	0.924695i
$567$	3.14188	+	3.93979i	0.131947	+	0.165456i
$568$	−33.2754			−1.39620
$569$	−8.90531	−	11.1669i	−0.373330	−	0.468141i	0.559305	−	0.828962i	$-0.311068\pi$
$569$	−8.90531	−	11.1669i	−0.373330	−	0.468141i	−0.932635	+	0.360821i	$0.882497\pi$
$570$	−0.200462	−	0.0965373i	−0.00839642	−	0.00404350i
$571$	6.56913	−	8.23743i	0.274909	−	0.344726i	−0.625141	−	0.780512i	$-0.714958\pi$
$571$	6.56913	−	8.23743i	0.274909	−	0.344726i	0.900050	+	0.435787i	$0.143530\pi$
$572$	6.89153	−	8.64171i	0.288149	−	0.361328i
$573$	1.04603	−	0.503742i	0.0436986	−	0.0210441i
$574$	−5.70894	−	25.0125i	−0.238286	−	1.04400i
$575$	−7.92629	+	34.7274i	−0.330549	+	1.44823i
$576$	−5.11967	−	2.46550i	−0.213320	−	0.102729i
$577$	−7.60750	+	3.66358i	−0.316704	+	0.152517i	−0.585482	−	0.810686i	$-0.699095\pi$
$577$	−7.60750	+	3.66358i	−0.316704	+	0.152517i	0.268778	+	0.963202i	$0.413380\pi$
$578$	−1.09687	+	4.80572i	−0.0456239	+	0.199892i
$579$	−20.6010			−0.856148
$580$	0.747140	+	1.61862i	0.0310233	+	0.0672093i
$581$	31.6454			1.31287
$582$	−0.102449	+	0.448860i	−0.00424666	+	0.0186058i
$583$	10.8997	−	5.24903i	0.451420	−	0.217392i
$584$	29.5344	+	14.2230i	1.22214	+	0.588553i
$585$	−0.144298	+	0.632210i	−0.00596598	+	0.0261387i
$586$	−0.938757	−	4.11296i	−0.0387797	−	0.169905i
$587$	−8.42975	+	4.05955i	−0.347933	+	0.167556i	−0.599685	−	0.800236i	$-0.704708\pi$
$587$	−8.42975	+	4.05955i	−0.347933	+	0.167556i	0.251752	+	0.967792i	$0.418993\pi$
$588$	13.3206	−	16.7034i	0.549330	−	0.688839i
$589$	−1.73914	+	2.18082i	−0.0716602	+	0.0898590i
$590$	−1.10091	−	0.530169i	−0.0453237	−	0.0218267i
$591$	−3.21608	−	4.03284i	−0.132292	−	0.165889i
$592$	−0.124786			−0.00512866
$593$	−3.16050	−	3.96314i	−0.129786	−	0.162747i	0.712692	−	0.701477i	$-0.247476\pi$
$593$	−3.16050	−	3.96314i	−0.129786	−	0.162747i	−0.842478	+	0.538730i	$0.818904\pi$
$594$	0.852187	+	3.73368i	0.0349657	+	0.153195i
$595$	1.08925	+	4.77234i	0.0446551	+	0.195647i
$596$	16.3675	+	20.5242i	0.670439	+	0.840704i
$597$	2.80583			0.114835
$598$	9.40694	+	11.7959i	0.384679	+	0.482372i
$599$	−20.9430	−	10.0856i	−0.855707	−	0.412087i	−0.0460140	−	0.998941i	$-0.514652\pi$
$599$	−20.9430	−	10.0856i	−0.855707	−	0.412087i	−0.809693	+	0.586854i	$0.800366\pi$
$600$	8.87824	−	11.1330i	0.362452	−	0.454501i
$601$	−3.78317	+	4.74395i	−0.154319	+	0.193510i	−0.852981	−	0.521942i	$-0.825208\pi$
$601$	−3.78317	+	4.74395i	−0.154319	+	0.193510i	0.698662	+	0.715452i	$0.253779\pi$
$602$	32.8548	−	15.8220i	1.33906	−	0.644858i
$603$	0.632094	+	2.76938i	0.0257409	+	0.112778i
$604$	−1.71508	+	7.51427i	−0.0697857	+	0.305751i
$605$	−1.66706	−	0.802815i	−0.0677758	−	0.0326391i
$606$	3.71898	−	1.79097i	0.151073	−	0.0727531i
$607$	8.74796	−	38.3273i	0.355069	−	1.55566i	−0.410230	−	0.911982i	$-0.634552\pi$
$607$	8.74796	−	38.3273i	0.355069	−	1.55566i	0.765299	−	0.643675i	$-0.222591\pi$
$608$	−4.68033			−0.189813
$609$	11.3730	+	24.6386i	0.460857	+	0.998408i
$610$	1.81097			0.0733242
$611$	−3.30907	+	14.4980i	−0.133871	+	0.586526i
$612$	−3.56684	+	1.71770i	−0.144181	+	0.0694340i
$613$	−22.2460	−	10.7131i	−0.898506	−	0.432698i	−0.0731567	−	0.997320i	$-0.523307\pi$
$613$	−22.2460	−	10.7131i	−0.898506	−	0.432698i	−0.825349	+	0.564623i	$0.809022\pi$
$614$	0.571719	−	2.50487i	0.0230727	−	0.101088i
$615$	−0.352620	−	1.54493i	−0.0142190	−	0.0622976i
$616$	54.9708	−	26.4725i	2.21484	−	1.06661i
$617$	11.8195	−	14.8212i	0.475837	−	0.596680i	−0.484753	−	0.874651i	$-0.661090\pi$
$617$	11.8195	−	14.8212i	0.475837	−	0.596680i	0.960590	+	0.277971i	$0.0896618\pi$
$618$	4.63805	−	5.81594i	0.186570	−	0.233951i
$619$	25.7787	+	12.4143i	1.03613	+	0.498975i	0.873046	−	0.487637i	$-0.162141\pi$
$619$	25.7787	+	12.4143i	1.03613	+	0.498975i	0.163085	+	0.986612i	$0.447855\pi$
$620$	0.675303	+	0.846804i	0.0271208	+	0.0340085i
$621$	7.24173			0.290601
$622$	−8.97499	−	11.2543i	−0.359864	−	0.451256i
$623$	−6.39837	−	28.0331i	−0.256345	−	1.12312i
$624$	−0.165951	−	0.727081i	−0.00664338	−	0.0291065i
$625$	14.8317	+	18.5983i	0.593267	+	0.743933i
$626$	−16.6881			−0.666989
$627$	2.22318	+	2.78778i	0.0887852	+	0.111333i
$628$	−14.0015	−	6.74275i	−0.558719	−	0.269065i
$629$	−0.809022	+	1.01448i	−0.0322578	+	0.0404500i
$630$	−0.819951	+	1.02819i	−0.0326676	+	0.0409639i
$631$	−18.9321	+	9.11724i	−0.753676	+	0.362951i	−0.770947	−	0.636899i	$-0.780217\pi$
$631$	−18.9321	+	9.11724i	−0.753676	+	0.362951i	0.0172705	+	0.999851i	$0.494502\pi$
$632$	4.36078	+	19.1058i	0.173463	+	0.759989i
$633$	−1.07895	+	4.72718i	−0.0428844	+	0.187889i
$634$	1.55097	+	0.746907i	0.0615968	+	0.0296635i
$635$	4.36513	−	2.10214i	0.173225	−	0.0834207i
$636$	−0.747629	+	3.27558i	−0.0296454	+	0.129885i
$637$	41.8500			1.65816
$638$	−0.337120	+	20.6208i	−0.0133467	+	0.816385i
$639$	−11.4943			−0.454707
$640$	−0.366331	+	1.60500i	−0.0144805	+	0.0634432i
$641$	−5.46803	+	2.63327i	−0.215974	+	0.104008i	−0.538743	−	0.842470i	$-0.681101\pi$
$641$	−5.46803	+	2.63327i	−0.215974	+	0.104008i	0.322769	+	0.946478i	$0.395386\pi$
$642$	−7.85332	−	3.78196i	−0.309946	−	0.149262i
$643$	10.0678	−	44.1097i	0.397033	−	1.73952i	−0.241943	−	0.970291i	$-0.577785\pi$
$643$	10.0678	−	44.1097i	0.397033	−	1.73952i	0.638976	−	0.769226i	$-0.279358\pi$
$644$	−9.43203	−	41.3244i	−0.371674	−	1.62841i
$645$	2.02932	−	0.977270i	0.0799045	−	0.0384800i
$646$	1.65897	−	2.08028i	0.0652713	−	0.0818476i
$647$	−7.22803	+	9.06366i	−0.284163	+	0.356329i	−0.903342	−	0.428921i	$-0.858894\pi$
$647$	−7.22803	+	9.06366i	−0.284163	+	0.356329i	0.619179	+	0.785250i	$0.287465\pi$
$648$	−2.60826	−	1.25607i	−0.102462	−	0.0493431i
$649$	12.2094	+	15.3101i	0.479260	+	0.600973i
$650$	10.2479			0.401954
$651$	10.2795	+	12.8901i	0.402886	+	0.505202i
$652$	2.62503	+	11.5010i	0.102804	+	0.450415i
$653$	−2.81311	−	12.3250i	−0.110086	−	0.482316i	−0.999673	−	0.0255523i	$-0.991866\pi$
$653$	−2.81311	−	12.3250i	−0.110086	−	0.482316i	0.889588	−	0.456764i	$-0.150992\pi$
$654$	−4.24271	−	5.32019i	−0.165903	−	0.208036i
$655$	−3.61821			−0.141375
$656$	1.13628	+	1.42486i	0.0443645	+	0.0556313i
$657$	10.2021	+	4.91305i	0.398020	+	0.191676i
$658$	−18.8033	+	23.5786i	−0.733030	+	0.919190i
$659$	28.8673	−	36.1984i	1.12451	−	1.41009i	0.224360	−	0.974506i	$-0.427971\pi$
$659$	28.8673	−	36.1984i	1.12451	−	1.41009i	0.900148	−	0.435583i	$-0.143458\pi$
$660$	1.24744	−	0.600733i	0.0485564	−	0.0233835i
$661$	0.706721	+	3.09635i	0.0274882	+	0.120434i	0.986811	−	0.161879i	$-0.0517555\pi$
$661$	0.706721	+	3.09635i	0.0274882	+	0.120434i	−0.959322	+	0.282313i	$0.908898\pi$
$662$	1.25125	−	5.48207i	0.0486311	−	0.213067i
$663$	−6.98693	−	3.36473i	−0.271350	−	0.130675i
$664$	−16.3795	+	7.88794i	−0.635647	+	0.306112i
$665$	−0.272465	+	1.19375i	−0.0105657	+	0.0462915i
$666$	−0.348603			−0.0135081
$667$	37.8732	+	9.29819i	1.46646	+	0.360027i
$668$	−28.4919			−1.10239
$669$	2.31324	−	10.1350i	0.0894350	−	0.391840i
$670$	−0.667912	+	0.321649i	−0.0258037	+	0.0124264i
$671$	−26.1484	−	12.5924i	−1.00945	−	0.486124i
$672$	−6.15580	+	26.9703i	−0.237465	+	1.04040i
$673$	−2.51910	−	11.0369i	−0.0971043	−	0.425442i	0.902886	−	0.429880i	$-0.141444\pi$
$673$	−2.51910	−	11.0369i	−0.0971043	−	0.425442i	−0.999990	+	0.00443874i	$0.998587\pi$
$674$	−5.98287	+	2.88120i	−0.230451	+	0.110980i
$675$	3.06680	−	3.84565i	0.118041	−	0.148019i
$676$	5.66554	−	7.10436i	0.217905	−	0.273245i
$677$	−4.00868	−	1.93048i	−0.154066	−	0.0741943i	0.355262	−	0.934767i	$-0.384392\pi$
$677$	−4.00868	−	1.93048i	−0.154066	−	0.0741943i	−0.509328	+	0.860573i	$0.670106\pi$
$678$	2.41957	+	3.03404i	0.0929229	+	0.116522i
$679$	2.53370			0.0972345
$680$	−1.75335	−	2.19863i	−0.0672379	−	0.0843136i
$681$	−6.22713	−	27.2828i	−0.238624	−	1.04548i
$682$	2.78816	+	12.2157i	0.106764	+	0.467764i
$683$	15.5911	+	19.5506i	0.596577	+	0.748084i	0.984840	−	0.173465i	$-0.0554962\pi$
$683$	15.5911	+	19.5506i	0.596577	+	0.748084i	−0.388263	+	0.921549i	$0.626925\pi$
$684$	−0.990273			−0.0378640
$685$	1.73137	+	2.17107i	0.0661523	+	0.0829523i
$686$	47.3659	+	22.8102i	1.80844	+	0.870897i
$687$	2.17985	−	2.73345i	0.0831665	−	0.104287i
$688$	−1.61507	+	2.02523i	−0.0615740	+	0.0772114i
$689$	−5.92963	+	2.85556i	−0.225901	+	0.108788i
$690$	0.420544	+	1.84253i	0.0160099	+	0.0701438i
$691$	2.00976	−	8.80534i	0.0764549	−	0.334971i	−0.922206	−	0.386698i	$-0.873616\pi$
$691$	2.00976	−	8.80534i	0.0764549	−	0.334971i	0.998661	+	0.0517274i	$0.0164727\pi$
$692$	−23.1156	−	11.1319i	−0.878723	−	0.423171i
$693$	18.9885	−	9.14439i	0.721314	−	0.347367i
$694$	−0.307584	+	1.34761i	−0.0116757	+	0.0511548i
$695$	−3.55787			−0.134958
$696$	−12.0281	−	9.91800i	−0.455922	−	0.375941i
$697$	18.9506			0.717807
$698$	2.96912	−	13.0086i	0.112383	−	0.492381i
$699$	−3.02067	+	1.45468i	−0.114252	+	0.0550209i
$700$	−25.9393	−	12.4917i	−0.980413	−	0.472142i
$701$	5.98486	−	26.2214i	0.226045	−	0.990368i	−0.726785	−	0.686865i	$-0.758986\pi$
$701$	5.98486	−	26.2214i	0.226045	−	0.990368i	0.952830	−	0.303504i	$-0.0981564\pi$
$702$	−0.463604	−	2.03118i	−0.0174976	−	0.0766621i
$703$	−0.292430	+	0.140827i	−0.0110292	+	0.00531138i
$704$	−14.8178	+	18.5809i	−0.558466	+	0.700294i
$705$	−1.16141	+	1.45637i	−0.0437414	+	0.0548499i
$706$	−17.9889	−	8.66300i	−0.677021	−	0.326036i
$707$	−14.1632	−	17.7601i	−0.532661	−	0.667936i
$708$	−5.43844			−0.204389
$709$	−22.0688	−	27.6734i	−0.828811	−	1.03930i	−0.998551	−	0.0538071i	$-0.982864\pi$
$709$	−22.0688	−	27.6734i	−0.828811	−	1.03930i	0.169740	−	0.985489i	$-0.445707\pi$
$710$	−0.667500	−	2.92451i	−0.0250508	−	0.109755i
$711$	1.50634	+	6.59971i	0.0564922	+	0.247509i
$712$	10.2993	+	12.9149i	0.385983	+	0.484008i
$713$	23.6933			0.887320
$714$	−9.80563	−	12.2959i	−0.366966	−	0.460161i
$715$	2.44354	+	1.17675i	0.0913834	+	0.0440079i
$716$	−0.532330	+	0.667521i	−0.0198941	+	0.0249464i
$717$	11.4681	−	14.3805i	0.428282	−	0.537049i
$718$	6.97470	−	3.35884i	0.260293	−	0.125351i
$719$	−2.35378	−	10.3126i	−0.0877813	−	0.384595i	0.911884	−	0.410447i	$-0.134627\pi$
$719$	−2.35378	−	10.3126i	−0.0877813	−	0.384595i	−0.999666	+	0.0258519i	$0.991770\pi$
$720$	0.0207875	−	0.0910761i	0.000774706	−	0.00339421i
$721$	−36.8836	−	17.7622i	−1.37362	−	0.661499i
$722$	−15.0753	+	7.25988i	−0.561045	+	0.270185i
$723$	1.25172	−	5.48413i	0.0465518	−	0.203957i
$724$	−15.8857			−0.590386
$725$	20.9767	−	16.1745i	0.779053	−	0.600706i
$726$	5.94470			0.220628
$727$	−10.2003	+	44.6903i	−0.378307	+	1.65747i	0.324346	+	0.945938i	$0.394856\pi$
$727$	−10.2003	+	44.6903i	−0.378307	+	1.65747i	−0.702653	+	0.711532i	$0.748001\pi$
$728$	−29.9050	+	14.4015i	−1.10835	+	0.533755i
$729$	−0.900969	−	0.433884i	−0.0333692	−	0.0160698i
$730$	−0.657578	+	2.88104i	−0.0243380	+	0.106632i
$731$	5.99376	+	26.2604i	0.221687	+	0.971275i
$732$	7.26198	−	3.49719i	0.268411	−	0.129260i
$733$	−32.3666	+	40.5865i	−1.19549	+	1.49910i	−0.375396	+	0.926864i	$0.622493\pi$
$733$	−32.3666	+	40.5865i	−1.19549	+	1.49910i	−0.820093	+	0.572231i	$0.806078\pi$
$734$	3.93350	−	4.93245i	0.145188	−	0.182060i
$735$	4.72310	+	2.27452i	0.174214	+	0.0838970i
$736$	24.7871	+	31.0820i	0.913663	+	1.14570i
$737$	11.8804			0.437621
$738$	3.17434	+	3.98050i	0.116849	+	0.146524i
$739$	3.60556	+	15.7970i	0.132633	+	0.581102i	0.996942	+	0.0781419i	$0.0248987\pi$
$739$	3.60556	+	15.7970i	0.132633	+	0.581102i	−0.864309	+	0.502960i	$0.832244\pi$
$740$	0.0280444	+	0.122871i	0.00103093	+	0.00451681i
$741$	−1.20945	−	1.51660i	−0.0444301	−	0.0557136i
$742$	−13.3471			−0.489988
$743$	22.5216	+	28.2412i	0.826238	+	1.03607i	0.998696	+	0.0510523i	$0.0162575\pi$
$743$	22.5216	+	28.2412i	0.826238	+	1.03607i	−0.172458	+	0.985017i	$0.555171\pi$
$744$	−8.53362	−	4.10957i	−0.312858	−	0.150664i
$745$	−4.01612	+	5.03605i	−0.147139	+	0.184507i
$746$	10.9962	−	13.7889i	0.402601	−	0.504846i
$747$	−5.65795	+	2.72473i	−0.207014	+	0.0996926i
$748$	3.68440	+	16.1424i	0.134715	+	0.590224i
$749$	−10.6741	+	46.7663i	−0.390023	+	1.70880i
$750$	2.33220	+	1.12313i	0.0851600	+	0.0410109i
$751$	−37.5435	+	18.0800i	−1.36998	+	0.659748i	−0.966838	−	0.255389i	$-0.917797\pi$
$751$	−37.5435	+	18.0800i	−1.36998	+	0.659748i	−0.403143	+	0.915137i	$0.632082\pi$
$752$	0.476705	−	2.08858i	0.0173836	−	0.0761627i
$753$	26.8112			0.977054
$754$	0.183399	−	11.2181i	0.00667900	−	0.408538i
$755$	−1.89120			−0.0688279
$756$	−1.30245	+	5.70643i	−0.0473698	+	0.207541i
$757$	−7.04277	+	3.39162i	−0.255974	+	0.123271i	−0.557471	−	0.830197i	$-0.688228\pi$
$757$	−7.04277	+	3.39162i	−0.255974	+	0.123271i	0.301497	+	0.953467i	$0.402514\pi$
$758$	−28.8536	−	13.8952i	−1.04801	−	0.504695i
$759$	6.73961	−	29.5282i	0.244632	−	1.07180i
$760$	−0.156527	−	0.685792i	−0.00567785	−	0.0248763i
$761$	19.4919	−	9.38680i	0.706580	−	0.340271i	−0.0458451	−	0.998949i	$-0.514598\pi$
$761$	19.4919	−	9.38680i	0.706580	−	0.340271i	0.752426	+	0.658677i	$0.228884\pi$
$762$	−9.70520	+	12.1699i	−0.351582	+	0.440870i
$763$	−23.3486	+	29.2782i	−0.845275	+	1.05994i
$764$	1.21500	+	0.585113i	0.0439571	+	0.0211686i
$765$	−0.605658	−	0.759471i

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)

\(f(q)\)	\(=\)	\(q+(0.203758 - 0.892721i) q^{2} +(0.900969 - 0.433884i) q^{3} +(1.04650 + 0.503970i) q^{4} +(-0.0634200 + 0.277861i) q^{5} +(-0.203758 - 0.892721i) q^{6} +(-4.54015 + 2.18642i) q^{7} +(1.80497 - 2.26336i) q^{8} +(0.623490 - 0.781831i) q^{9} +O(q^{10})\)	\(q+(0.203758 - 0.892721i) q^{2} +(0.900969 - 0.433884i) q^{3} +(1.04650 + 0.503970i) q^{4} +(-0.0634200 + 0.277861i) q^{5} +(-0.203758 - 0.892721i) q^{6} +(-4.54015 + 2.18642i) q^{7} +(1.80497 - 2.26336i) q^{8} +(0.623490 - 0.781831i) q^{9} +(0.235130 + 0.113233i) q^{10} +(-2.60766 - 3.26990i) q^{11} +1.16153 q^{12} +(1.41861 + 1.77888i) q^{13} +(1.02677 + 4.49858i) q^{14} +(0.0634200 + 0.277861i) q^{15} +(-0.204365 - 0.256265i) q^{16} -3.40834 q^{17} +(-0.570916 - 0.715906i) q^{18} +(-0.768127 - 0.369911i) q^{19} +(-0.206403 + 0.258821i) q^{20} +(-3.14188 + 3.93979i) q^{21} +(-3.45044 + 1.66164i) q^{22} +(1.61144 + 7.06017i) q^{23} +(0.644186 - 2.82237i) q^{24} +(4.43166 + 2.13417i) q^{25} +(1.87710 - 0.903962i) q^{26} +(0.222521 - 0.974928i) q^{27} -5.85318 q^{28} +(2.41553 - 4.81302i) q^{29} +0.260975 q^{30} +(0.728037 - 3.18974i) q^{31} +(4.94610 - 2.38192i) q^{32} +(-3.76817 - 1.81466i) q^{33} +(-0.694475 + 3.04269i) q^{34} +(-0.319585 - 1.40019i) q^{35} +(1.04650 - 0.503970i) q^{36} +(0.237365 - 0.297647i) q^{37} +(-0.486739 + 0.610351i) q^{38} +(2.04995 + 0.987204i) q^{39} +(0.514429 + 0.645074i) q^{40} -5.56008 q^{41} +(2.87695 + 3.60758i) q^{42} +(-1.75856 - 7.70474i) q^{43} +(-1.08099 - 4.73615i) q^{44} +(0.177699 + 0.222827i) q^{45} +6.63110 q^{46} +(4.07504 + 5.10993i) q^{47} +(-0.295316 - 0.142216i) q^{48} +(11.4681 - 14.3805i) q^{49} +(2.80821 - 3.52138i) q^{50} +(-3.07081 + 1.47882i) q^{51} +(0.588079 + 2.57654i) q^{52} +(-0.643658 + 2.82005i) q^{53} +(-0.824998 - 0.397298i) q^{54} +(1.07396 - 0.517190i) q^{55} +(-3.24617 + 14.2224i) q^{56} -0.852557 q^{57} +(-3.80450 - 3.13709i) q^{58} -4.68212 q^{59} +(-0.0736644 + 0.322745i) q^{60} +(6.25207 - 3.01084i) q^{61} +(-2.69920 - 1.29987i) q^{62} +(-1.12132 + 4.91284i) q^{63} +(-1.26445 - 5.53994i) q^{64} +(-0.584250 + 0.281360i) q^{65} +(-2.38778 + 2.99418i) q^{66} +(-1.77109 + 2.22087i) q^{67} +(-3.56684 - 1.71770i) q^{68} +(4.51515 + 5.66182i) q^{69} -1.31510 q^{70} +(-7.16657 - 8.98660i) q^{71} +(-0.644186 - 2.82237i) q^{72} +(2.51970 + 11.0395i) q^{73} +(-0.217350 - 0.272549i) q^{74} +4.91877 q^{75} +(-0.617425 - 0.774227i) q^{76} +(18.9885 + 9.14439i) q^{77} +(1.29899 - 1.62888i) q^{78} +(-4.22068 + 5.29256i) q^{79} +(0.0841670 - 0.0405327i) q^{80} +(-0.222521 - 0.974928i) q^{81} +(-1.13291 + 4.96360i) q^{82} +(-5.65795 - 2.72473i) q^{83} +(-5.27353 + 2.53960i) q^{84} +(0.216157 - 0.947045i) q^{85} -7.23650 q^{86} +(0.0880280 - 5.38445i) q^{87} -12.1077 q^{88} +(-1.26972 + 5.56302i) q^{89} +(0.235130 - 0.113233i) q^{90} +(-10.3301 - 4.97470i) q^{91} +(-1.87174 + 8.20062i) q^{92} +(-0.728037 - 3.18974i) q^{93} +(5.39206 - 2.59668i) q^{94} +(0.151498 - 0.189973i) q^{95} +(3.42281 - 4.29207i) q^{96} +(-0.453007 - 0.218157i) q^{97} +(-10.5011 - 13.1679i) q^{98} -4.18236 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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