LMFDB - Embedded newform 81.2.g.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	81.13
Dual form			81.2.g.a.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.94437 + 0.976500i) q^{2} +(-1.52821 + 0.815208i) q^{3} +(1.63271 + 2.19311i) q^{4} +(-0.185416 - 0.619334i) q^{5} +(-3.76746 + 0.0927672i) q^{6} +(-0.724564 - 1.67973i) q^{7} +(0.277373 + 1.57306i) q^{8} +(1.67087 - 2.49162i) q^{9} +(0.244261 - 1.38527i) q^{10} +(-1.17723 + 0.279008i) q^{11} +(-4.28297 - 2.02054i) q^{12} +(4.45604 + 2.93078i) q^{13} +(0.231433 - 3.97355i) q^{14} +(0.788242 + 0.795322i) q^{15} +(0.571538 - 1.90907i) q^{16} +(-6.43434 + 2.34191i) q^{17} +(5.68186 - 3.21304i) q^{18} +(-5.97823 - 2.17590i) q^{19} +(1.05554 - 1.41783i) q^{20} +(2.47662 + 1.97631i) q^{21} +(-2.56142 - 0.607068i) q^{22} +(-1.23445 + 2.86177i) q^{23} +(-1.70626 - 2.17786i) q^{24} +(3.82824 - 2.51788i) q^{25} +(5.80229 + 10.0499i) q^{26} +(-0.522256 + 5.16984i) q^{27} +(2.50083 - 4.33156i) q^{28} +(0.342261 + 5.87639i) q^{29} +(0.756004 + 2.31612i) q^{30} +(2.75457 - 0.321963i) q^{31} +(5.16779 - 5.47754i) q^{32} +(1.57161 - 1.38607i) q^{33} +(-14.7976 - 1.72959i) q^{34} +(-0.905967 + 0.760197i) q^{35} +(8.19245 - 0.403694i) q^{36} +(-1.09453 - 0.918418i) q^{37} +(-9.49913 - 10.0685i) q^{38} +(-9.19898 - 0.846262i) q^{39} +(0.922821 - 0.463458i) q^{40} +(0.996758 - 0.500591i) q^{41} +(2.88559 + 6.26110i) q^{42} +(6.61155 + 7.00783i) q^{43} +(-2.53397 - 2.12625i) q^{44} +(-1.85295 - 0.572840i) q^{45} +(-5.19473 + 4.35890i) q^{46} +(-6.06108 - 0.708439i) q^{47} +(0.682857 + 3.38339i) q^{48} +(2.50720 - 2.65747i) q^{49} +(9.90223 - 1.15740i) q^{50} +(7.92390 - 8.82426i) q^{51} +(0.847890 + 14.5577i) q^{52} +(4.26135 - 7.38088i) q^{53} +(-6.06381 + 9.54211i) q^{54} +(0.391077 + 0.677365i) q^{55} +(2.44134 - 1.60569i) q^{56} +(10.9098 - 1.54827i) q^{57} +(-5.07281 + 11.7601i) q^{58} +(2.03183 + 0.481552i) q^{59} +(-0.457257 + 3.02723i) q^{60} +(-2.14382 + 2.87965i) q^{61} +(5.67029 + 2.06382i) q^{62} +(-5.39591 - 1.00127i) q^{63} +(11.6517 - 4.24088i) q^{64} +(0.988911 - 3.30319i) q^{65} +(4.40929 - 1.16036i) q^{66} +(-0.0709235 + 1.21771i) q^{67} +(-15.6415 - 10.2876i) q^{68} +(-0.446439 - 5.37972i) q^{69} +(-2.50387 + 0.593428i) q^{70} +(1.41528 - 8.02646i) q^{71} +(4.38293 + 1.93727i) q^{72} +(1.11524 + 6.32482i) q^{73} +(-1.23133 - 2.85455i) q^{74} +(-3.79778 + 6.96867i) q^{75} +(-4.98873 - 16.6635i) q^{76} +(1.32164 + 1.77527i) q^{77} +(-17.0599 - 10.6283i) q^{78} +(-12.7417 - 6.39915i) q^{79} -1.28832 q^{80} +(-3.41638 - 8.32637i) q^{81} +2.42689 q^{82} +(6.00472 + 3.01569i) q^{83} +(-0.290674 + 8.65824i) q^{84} +(2.64346 + 3.55078i) q^{85} +(6.01216 + 20.0820i) q^{86} +(-5.31353 - 8.70136i) q^{87} +(-0.765429 - 1.77446i) q^{88} +(-2.70557 - 15.3441i) q^{89} +(-3.04345 - 2.92322i) q^{90} +(1.69423 - 9.60848i) q^{91} +(-8.29166 + 1.96516i) q^{92} +(-3.94710 + 2.73757i) q^{93} +(-11.0932 - 7.29611i) q^{94} +(-0.239145 + 4.10597i) q^{95} +(-3.43215 + 12.5837i) q^{96} +(1.06957 - 3.57262i) q^{97} +(7.46994 - 2.71884i) q^{98} +(-1.27181 + 3.39940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

Coefficient data

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

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

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

$2$	1.94437	+	0.976500i	1.37488	+	0.690490i	0.974191	−	0.225725i	$-0.0724752\pi$
$2$	1.94437	+	0.976500i	1.37488	+	0.690490i	0.400687	+	0.916215i	$0.368771\pi$
$3$	−1.52821	+	0.815208i	−0.882314	+	0.470661i
$3$	−1.52821	+	0.815208i	−0.882314	+	0.470661i
$4$	1.63271	+	2.19311i	0.816355	+	1.09656i
$5$	−0.185416	−	0.619334i	−0.0829208	−	0.276975i	0.906466	−	0.422278i	$-0.138769\pi$
$5$	−0.185416	−	0.619334i	−0.0829208	−	0.276975i	−0.989387	+	0.145303i	$0.953584\pi$
$6$	−3.76746	+	0.0927672i	−1.53806	+	0.0378720i
$7$	−0.724564	−	1.67973i	−0.273860	−	0.634878i	0.724670	−	0.689097i	$-0.241992\pi$
$7$	−0.724564	−	1.67973i	−0.273860	−	0.634878i	−0.998529	+	0.0542188i	$0.982733\pi$
$8$	0.277373	+	1.57306i	0.0980662	+	0.556161i
$9$	1.67087	−	2.49162i	0.556957	−	0.830541i
$10$	0.244261	−	1.38527i	0.0772422	−	0.438062i
$11$	−1.17723	+	0.279008i	−0.354948	+	0.0841242i	−0.404222	−	0.914661i	$-0.632458\pi$
$11$	−1.17723	+	0.279008i	−0.354948	+	0.0841242i	0.0492736	+	0.998785i	$0.484309\pi$
$12$	−4.28297	−	2.02054i	−1.23639	−	0.583280i
$13$	4.45604	+	2.93078i	1.23588	+	0.812853i	0.987776	−	0.155879i	$-0.0498211\pi$
$13$	4.45604	+	2.93078i	1.23588	+	0.812853i	0.248107	+	0.968733i	$0.420191\pi$
$14$	0.231433	−	3.97355i	0.0618531	−	1.06198i
$15$	0.788242	+	0.795322i	0.203523	+	0.205351i
$16$	0.571538	−	1.90907i	0.142885	−	0.477268i
$17$	−6.43434	+	2.34191i	−1.56056	+	0.567996i	−0.970864	−	0.239631i	$-0.922973\pi$
$17$	−6.43434	+	2.34191i	−1.56056	+	0.567996i	−0.589693	+	0.807628i	$0.700751\pi$
$18$	5.68186	−	3.21304i	1.33923	−	0.757320i
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.451909	−	0.892064i	$-0.649257\pi$
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.919590	+	0.392879i	$0.871479\pi$
$20$	1.05554	−	1.41783i	0.236025	−	0.317037i
$21$	2.47662	+	1.97631i	0.540442	+	0.431267i
$22$	−2.56142	−	0.607068i	−0.546097	−	0.129427i
$23$	−1.23445	+	2.86177i	−0.257400	+	0.596719i	−0.997090	−	0.0762275i	$-0.975712\pi$
$23$	−1.23445	+	2.86177i	−0.257400	+	0.596719i	0.739691	+	0.672947i	$0.234972\pi$
$24$	−1.70626	−	2.17786i	−0.348288	−	0.444553i
$25$	3.82824	−	2.51788i	0.765649	−	0.503575i
$26$	5.80229	+	10.0499i	1.13792	+	1.97094i
$27$	−0.522256	+	5.16984i	−0.100508	+	0.994936i
$28$	2.50083	−	4.33156i	0.472612	−	0.818588i
$29$	0.342261	+	5.87639i	0.0635562	+	1.09122i	0.867799	+	0.496916i	$0.165534\pi$
$29$	0.342261	+	5.87639i	0.0635562	+	1.09122i	−0.804242	+	0.594301i	$0.797429\pi$
$30$	0.756004	+	2.31612i	0.138027	+	0.422864i
$31$	2.75457	−	0.321963i	0.494735	−	0.0578262i	0.134932	−	0.990855i	$-0.456918\pi$
$31$	2.75457	−	0.321963i	0.494735	−	0.0578262i	0.359802	+	0.933029i	$0.382844\pi$
$32$	5.16779	−	5.47754i	0.913546	−	0.968302i
$33$	1.57161	−	1.38607i	0.273582	−	0.241284i
$34$	−14.7976	−	1.72959i	−2.53777	−	0.296623i
$35$	−0.905967	+	0.760197i	−0.153136	+	0.128497i
$36$	8.19245	−	0.403694i	1.36541	−	0.0672824i
$37$	−1.09453	−	0.918418i	−0.179939	−	0.150987i	0.548369	−	0.836236i	$-0.315249\pi$
$37$	−1.09453	−	0.918418i	−0.179939	−	0.150987i	−0.728309	+	0.685249i	$0.759693\pi$
$38$	−9.49913	−	10.0685i	−1.54096	−	1.63332i
$39$	−9.19898	−	0.846262i	−1.47302	−	0.135510i
$40$	0.922821	−	0.463458i	0.145911	−	0.0732791i
$41$	0.996758	−	0.500591i	0.155667	−	0.0781791i	−0.369260	−	0.929326i	$-0.620389\pi$
$41$	0.996758	−	0.500591i	0.155667	−	0.0781791i	0.524927	+	0.851147i	$0.324092\pi$
$42$	2.88559	+	6.26110i	0.445257	+	0.966109i
$43$	6.61155	+	7.00783i	1.00825	+	1.06868i	0.997635	+	0.0687407i	$0.0218981\pi$
$43$	6.61155	+	7.00783i	1.00825	+	1.06868i	0.0106171	+	0.999944i	$0.496620\pi$
$44$	−2.53397	−	2.12625i	−0.382010	−	0.320545i
$45$	−1.85295	−	0.572840i	−0.276222	−	0.0853939i
$46$	−5.19473	+	4.35890i	−0.765922	+	0.642685i
$47$	−6.06108	−	0.708439i	−0.884099	−	0.103336i	−0.338088	−	0.941114i	$-0.609780\pi$
$47$	−6.06108	−	0.708439i	−0.884099	−	0.103336i	−0.546011	+	0.837778i	$0.683854\pi$
$48$	0.682857	+	3.38339i	0.0985620	+	0.488350i
$49$	2.50720	−	2.65747i	0.358171	−	0.379639i
$50$	9.90223	−	1.15740i	1.40039	−	0.163682i
$51$	7.92390	−	8.82426i	1.10957	−	1.23564i
$52$	0.847890	+	14.5577i	0.117581	+	2.01879i
$53$	4.26135	−	7.38088i	0.585342	−	1.01384i	−0.409491	−	0.912314i	$-0.634294\pi$
$53$	4.26135	−	7.38088i	0.585342	−	1.01384i	0.994833	−	0.101528i	$-0.0323731\pi$
$54$	−6.06381	+	9.54211i	−0.825180	+	1.29852i
$55$	0.391077	+	0.677365i	0.0527328	+	0.0913359i
$56$	2.44134	−	1.60569i	0.326238	−	0.214570i
$57$	10.9098	−	1.54827i	1.44504	−	0.205073i
$58$	−5.07281	+	11.7601i	−0.666093	+	1.54418i
$59$	2.03183	+	0.481552i	0.264521	+	0.0626927i	0.360736	−	0.932668i	$-0.382525\pi$
$59$	2.03183	+	0.481552i	0.264521	+	0.0626927i	−0.0962148	+	0.995361i	$0.530674\pi$
$60$	−0.457257	+	3.02723i	−0.0590316	+	0.390814i
$61$	−2.14382	+	2.87965i	−0.274488	+	0.368702i	−0.917895	−	0.396822i	$-0.870113\pi$
$61$	−2.14382	+	2.87965i	−0.274488	+	0.368702i	0.643407	+	0.765524i	$0.277520\pi$
$62$	5.67029	+	2.06382i	0.720128	+	0.262105i
$63$	−5.39591	−	1.00127i	−0.679820	−	0.126148i
$64$	11.6517	−	4.24088i	1.45646	−	0.530110i
$65$	0.988911	−	3.30319i	0.122659	−	0.409711i
$66$	4.40929	−	1.16036i	0.542746	−	0.142831i
$67$	−0.0709235	+	1.21771i	−0.00866469	+	0.148767i	0.991201	+	0.132367i	$0.0422576\pi$
$67$	−0.0709235	+	1.21771i	−0.00866469	+	0.148767i	−0.999866	+	0.0164003i	$0.994779\pi$
$68$	−15.6415	−	10.2876i	−1.89681	−	1.24755i
$69$	−0.446439	−	5.37972i	−0.0537450	−	0.647642i
$70$	−2.50387	+	0.593428i	−0.299270	+	0.0709282i
$71$	1.41528	−	8.02646i	0.167963	−	0.952565i	−0.777994	−	0.628272i	$-0.783763\pi$
$71$	1.41528	−	8.02646i	0.167963	−	0.952565i	0.945957	−	0.324293i	$-0.105126\pi$
$72$	4.38293	+	1.93727i	0.516533	+	0.228310i
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	0.977870	+	0.209215i	$0.0670909\pi$
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	−0.847341	+	0.531049i	$0.821798\pi$
$74$	−1.23133	−	2.85455i	−0.143140	−	0.331835i
$75$	−3.79778	+	6.96867i	−0.438530	+	0.804672i
$76$	−4.98873	−	16.6635i	−0.572247	−	1.91144i
$77$	1.32164	+	1.77527i	0.150614	+	0.202310i
$78$	−17.0599	−	10.6283i	−1.93165	−	1.20341i
$79$	−12.7417	−	6.39915i	−1.43356	−	0.719960i	−0.448759	−	0.893653i	$-0.648134\pi$
$79$	−12.7417	−	6.39915i	−1.43356	−	0.719960i	−0.984800	+	0.173693i	$0.944430\pi$
$80$	−1.28832			−0.144039
$81$	−3.41638	−	8.32637i	−0.379598	−	0.925152i
$82$	2.42689			0.268006
$83$	6.00472	+	3.01569i	0.659104	+	0.331015i	0.746719	−	0.665140i	$-0.231628\pi$
$83$	6.00472	+	3.01569i	0.659104	+	0.331015i	−0.0876146	+	0.996154i	$0.527924\pi$
$84$	−0.290674	+	8.65824i	−0.0317152	+	0.944692i
$85$	2.64346	+	3.55078i	0.286723	+	0.385136i
$86$	6.01216	+	20.0820i	0.648308	+	2.16550i
$87$	−5.31353	−	8.70136i	−0.569670	−	0.932884i
$88$	−0.765429	−	1.77446i	−0.0815950	−	0.189158i
$89$	−2.70557	−	15.3441i	−0.286790	−	1.62647i	−0.698820	−	0.715297i	$-0.746291\pi$
$89$	−2.70557	−	15.3441i	−0.286790	−	1.62647i	0.412030	−	0.911170i	$-0.364820\pi$
$90$	−3.04345	−	2.92322i	−0.320808	−	0.308135i
$91$	1.69423	−	9.60848i	0.177604	−	1.00724i
$92$	−8.29166	+	1.96516i	−0.864465	+	0.204882i
$93$	−3.94710	+	2.73757i	−0.409295	+	0.283873i
$94$	−11.0932	−	7.29611i	−1.14418	−	0.752536i
$95$	−0.239145	+	4.10597i	−0.0245358	+	0.421263i
$96$	−3.43215	+	12.5837i	−0.350293	+	1.28432i
$97$	1.06957	−	3.57262i	0.108599	−	0.362745i	−0.886364	−	0.462989i	$-0.846777\pi$
$97$	1.06957	−	3.57262i	0.108599	−	0.362745i	0.994963	+	0.100244i	$0.0319622\pi$
$98$	7.46994	−	2.71884i	0.754578	−	0.274644i
$99$	−1.27181	+	3.39940i	−0.127822	+	0.341652i
$100$	11.7724	+	4.28480i	1.17724	+	0.428480i
$101$	−2.77713	+	3.73034i	−0.276335	+	0.371182i	−0.918525	−	0.395363i	$-0.870619\pi$
$101$	−2.77713	+	3.73034i	−0.276335	+	0.371182i	0.642190	+	0.766546i	$0.278026\pi$
$102$	24.0239	−	9.41995i	2.37872	−	0.932714i
$103$	5.02919	+	1.19194i	0.495541	+	0.117445i	0.470785	−	0.882248i	$-0.343971\pi$
$103$	5.02919	+	1.19194i	0.495541	+	0.117445i	0.0247562	+	0.999694i	$0.492119\pi$
$104$	−3.37432	+	7.82254i	−0.330879	+	0.767063i
$105$	0.764793	−	1.90029i	0.0746361	−	0.185450i
$106$	15.4931	−	10.1900i	1.50482	−	0.989737i
$107$	6.49528	+	11.2502i	0.627922	+	1.08759i	0.987968	+	0.154659i	$0.0494278\pi$
$107$	6.49528	+	11.2502i	0.627922	+	1.08759i	−0.360046	+	0.932935i	$0.617239\pi$
$108$	−12.1907	+	7.29549i	−1.17305	+	0.702008i
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	−0.905443	−	0.424469i	$-0.860461\pi$
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	0.820322	+	0.571902i	$0.193794\pi$
$110$	0.0989518	+	1.69894i	0.00943468	+	0.161987i
$111$	2.42138	+	0.511271i	0.229827	+	0.0485277i
$112$	−3.62084	+	0.423215i	−0.342137	+	0.0399901i
$113$	−9.53060	+	10.1018i	−0.896563	+	0.950302i	−0.999012	−	0.0444366i	$-0.985851\pi$
$113$	−9.53060	+	10.1018i	−0.896563	+	0.950302i	0.102449	+	0.994738i	$0.467332\pi$
$114$	22.7246	+	7.64303i	2.12835	+	0.715835i
$115$	2.00128	+	0.233916i	0.186620	+	0.0218127i
$116$	−12.3288	+	10.3451i	−1.14470	+	0.960514i
$117$	14.7479	−	6.20581i	1.36344	−	0.573728i
$118$	3.48039	+	2.92040i	0.320396	+	0.268844i
$119$	8.59586	+	9.11108i	0.787982	+	0.835212i
$120$	−1.03245	+	1.46055i	−0.0942495	+	0.133330i
$121$	−8.52194	+	4.27988i	−0.774722	+	0.389080i
$122$	−6.98037	+	3.50567i	−0.631973	+	0.317389i
$123$	−1.11517	+	1.57757i	−0.100552	+	0.142245i
$124$	5.20351	+	5.51539i	0.467289	+	0.495297i
$125$	−4.74544	−	3.98190i	−0.424445	−	0.356152i
$126$	−9.51390	−	7.21594i	−0.847566	−	0.642847i
$127$	−8.72949	+	7.32491i	−0.774617	+	0.649981i	−0.941887	−	0.335930i	$-0.890949\pi$
$127$	−8.72949	+	7.32491i	−0.774617	+	0.649981i	0.167270	+	0.985911i	$0.446505\pi$
$128$	11.8372	+	1.38357i	1.04627	+	0.122291i
$129$	−15.8167	−	5.31967i	−1.39258	−	0.468371i
$130$	5.14838	−	5.45696i	0.451543	−	0.478607i
$131$	14.4822	−	1.69272i	1.26531	−	0.147894i	0.543160	−	0.839629i	$-0.317228\pi$
$131$	14.4822	−	1.69272i	1.26531	−	0.147894i	0.722151	+	0.691735i	$0.243153\pi$
$132$	5.60578	+	1.18366i	0.487921	+	0.103024i
$133$	0.676693	+	11.6184i	0.0586768	+	1.00744i
$134$	−1.32700	+	2.29842i	−0.114635	+	0.198554i
$135$	3.29869	−	0.635123i	0.283906	−	0.0546627i
$136$	−5.46868	−	9.47202i	−0.468935	−	0.812219i
$137$	0.309806	−	0.203762i	0.0264685	−	0.0174086i	−0.536206	−	0.844087i	$-0.680143\pi$
$137$	0.309806	−	0.203762i	0.0264685	−	0.0174086i	0.562674	+	0.826679i	$0.309773\pi$
$138$	4.38525	−	10.8961i	0.373297	−	0.927539i
$139$	5.93229	−	13.7526i	0.503170	−	1.16648i	−0.457606	−	0.889155i	$-0.651293\pi$
$139$	5.93229	−	13.7526i	0.503170	−	1.16648i	0.960776	−	0.277325i	$-0.0894479\pi$
$140$	−3.14638	−	0.745705i	−0.265917	−	0.0630236i
$141$	9.84015	−	3.85840i	0.828690	−	0.324936i
$142$	10.5897	−	14.2244i	0.888665	−	1.19368i
$143$	−6.06349	−	2.20693i	−0.507055	−	0.184553i
$144$	−3.80172	−	4.61387i	−0.316810	−	0.384489i
$145$	3.57599	−	1.30155i	0.296970	−	0.108088i
$146$	−4.00775	+	13.3868i	−0.331684	+	1.10790i
$147$	−1.66514	+	6.10507i	−0.137338	+	0.503538i
$148$	0.227145	−	3.89993i	0.0186712	−	0.320572i
$149$	0.835701	+	0.549649i	0.0684633	+	0.0450290i	0.583279	−	0.812272i	$-0.301769\pi$
$149$	0.835701	+	0.549649i	0.0684633	+	0.0450290i	−0.514816	+	0.857301i	$0.672140\pi$
$150$	−14.1892	+	9.84114i	−1.15854	+	0.803526i
$151$	0.0191032	−	0.00452754i	0.00155460	−	0.000368446i	−0.229838	−	0.973229i	$-0.573820\pi$
$151$	0.0191032	−	0.00452754i	0.00155460	−	0.000368446i	0.231393	+	0.972860i	$0.425672\pi$
$152$	1.76462	−	10.0076i	0.143129	−	0.811727i
$153$	−4.91580	+	19.9450i	−0.397419	+	1.61246i
$154$	0.836205	+	4.74235i	0.0673833	+	0.382150i
$155$	−0.710144	−	1.64630i	−0.0570402	−	0.132234i
$156$	−13.1633	−	21.5561i	−1.05391	−	1.72587i
$157$	2.23838	+	7.47669i	0.178642	+	0.596705i	0.999667	+	0.0258129i	$0.00821741\pi$
$157$	2.23838	+	7.47669i	0.178642	+	0.596705i	−0.821025	+	0.570892i	$0.806597\pi$
$158$	−18.5259	−	24.8846i	−1.47384	−	1.97972i
$159$	−0.495303	+	14.7535i	−0.0392801	+	1.17003i
$160$	−4.35062	−	2.18497i	−0.343947	−	0.172737i
$161$	5.70142			0.449335
$162$	1.48799	−	19.5256i	0.116907	−	1.53408i
$163$	−15.3947			−1.20581			−0.602905	−	0.797813i	$-0.705990\pi$
$163$	−15.3947			−1.20581			−0.602905	+	0.797813i	$0.705990\pi$
$164$	2.72527	+	1.36868i	0.212808	+	0.106876i
$165$	−1.14984	−	0.716350i	−0.0895152	−	0.0557677i
$166$	8.73060	+	11.7272i	0.677626	+	0.910209i
$167$	−1.04821	−	3.50128i	−0.0811132	−	0.270937i	0.907806	−	0.419390i	$-0.137756\pi$
$167$	−1.04821	−	3.50128i	−0.0811132	−	0.270937i	−0.988919	+	0.148453i	$0.952571\pi$
$168$	−2.42191	+	4.44404i	−0.186855	+	0.342866i
$169$	6.11777	+	14.1826i	0.470597	+	1.09097i
$170$	1.67253	+	9.48537i	0.128277	+	0.727494i
$171$	−15.4104	+	11.2598i	−1.17846	+	0.861062i
$172$	−4.57421	+	25.9416i	−0.348780	+	1.97803i
$173$	12.9245	−	3.06317i	0.982635	−	0.232889i	0.292259	−	0.956339i	$-0.405593\pi$
$173$	12.9245	−	3.06317i	0.982635	−	0.232889i	0.690376	+	0.723450i	$0.257445\pi$
$174$	−1.83459	−	22.1073i	−0.139080	−	1.67595i
$175$	−7.00316	−	4.60605i	−0.529389	−	0.348185i
$176$	−0.140185	+	2.40688i	−0.0105668	+	0.181425i
$177$	−3.49763	+	0.920449i	−0.262898	+	0.0691852i
$178$	9.72284	−	32.4765i	0.728758	−	2.43422i
$179$	−0.392738	+	0.142945i	−0.0293546	+	0.0106842i	−0.356656	−	0.934236i	$-0.616083\pi$
$179$	−0.392738	+	0.142945i	−0.0293546	+	0.0106842i	0.327301	+	0.944920i	$0.393861\pi$
$180$	−1.76904	−	4.99902i	−0.131856	−	0.372605i
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.511717	−	0.859154i	$-0.670990\pi$
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.944252	+	0.329225i	$0.893213\pi$
$182$	12.6769	−	17.0280i	0.939675	−	1.26220i
$183$	0.928701	−	6.14839i	0.0686516	−	0.454502i
$184$	−4.84413	−	1.14808i	−0.357114	−	0.0846376i
$185$	−0.365864	+	0.848169i	−0.0268989	+	0.0623586i
$186$	−10.3479	+	1.46852i	−0.758742	+	0.107677i
$187$	6.92128	−	4.55220i	0.506134	−	0.332890i
$188$	−8.34230	−	14.4493i	−0.608425	−	1.05382i
$189$	9.06234	−	2.86863i	0.659188	−	0.208662i
$190$	−4.47446	+	7.75000i	−0.324612	+	0.562244i
$191$	−0.400574	−	6.87758i	−0.0289845	−	0.497645i	−0.981295	−	0.192512i	$-0.938336\pi$
$191$	−0.400574	−	6.87758i	−0.0289845	−	0.497645i	0.952310	−	0.305132i	$-0.0987006\pi$
$192$	−14.3491	+	15.9795i	−1.03556	+	1.15322i
$193$	8.68725	−	1.01539i	0.625322	−	0.0730897i	0.202470	−	0.979288i	$-0.435103\pi$
$193$	8.68725	−	1.01539i	0.625322	−	0.0730897i	0.422852	+	0.906199i	$0.361029\pi$
$194$	5.56831	−	5.90207i	0.399782	−	0.423744i
$195$	1.18152	+	5.85415i	0.0846106	+	0.419225i
$196$	9.92166	+	1.15968i	0.708690	+	0.0828339i
$197$	−6.47094	+	5.42976i	−0.461035	+	0.386855i	−0.843512	−	0.537111i	$-0.819516\pi$
$197$	−6.47094	+	5.42976i	−0.461035	+	0.386855i	0.382476	+	0.923965i	$0.375071\pi$
$198$	−5.79239	+	5.36777i	−0.411647	+	0.381471i
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	0.917561	−	0.397595i	$-0.130155\pi$
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	−0.232222	+	0.972663i	$0.574599\pi$
$200$	5.02262	+	5.32367i	0.355153	+	0.376440i
$201$	−0.884301	−	1.91874i	−0.0623738	−	0.135337i
$202$	−9.04245	+	4.54129i	−0.636225	+	0.319524i
$203$	9.62275	−	4.83272i	0.675384	−	0.339191i
$204$	32.2900	+	2.97053i	2.26075	+	0.207979i
$205$	−0.494848	−	0.524508i	−0.0345617	−	0.0366333i
$206$	8.61468	+	7.22858i	0.600213	+	0.503639i
$207$	5.06784	+	7.85741i	0.352239	+	0.546128i
$208$	8.14187	−	6.83184i	0.564537	−	0.473703i
$209$	7.64484	+	0.893553i	0.528804	+	0.0618084i
$210$	3.34268	−	2.94806i	0.230667	−	0.203435i
$211$	3.89505	−	4.12851i	0.268146	−	0.284218i	−0.579283	−	0.815126i	$-0.696668\pi$
$211$	3.89505	−	4.12851i	0.268146	−	0.284218i	0.847429	+	0.530908i	$0.178149\pi$
$212$	23.1446	−	2.70522i	1.58958	−	0.185795i
$213$	4.38038	+	13.4199i	0.300139	+	0.919515i
$214$	1.64346	+	28.2171i	0.112345	+	1.92888i
$215$	3.11430	−	5.39413i	0.212393	−	0.367876i
$216$	−8.27733	+	0.612434i	−0.563201	+	0.0416709i
$217$	−2.53667	−	4.39364i	−0.172200	−	0.298260i
$218$	−3.23101	+	2.12507i	−0.218832	+	0.143928i
$219$	−6.86036	−	8.75652i	−0.463580	−	0.591711i
$220$	−0.847021	+	1.96362i	−0.0571062	+	0.132387i
$221$	−35.5353	−	8.42202i	−2.39036	−	0.566527i
$222$	4.20880	+	3.35857i	0.282476	+	0.225413i
$223$	4.49831	−	6.04228i	0.301229	−	0.404621i	−0.625576	−	0.780163i	$-0.715136\pi$
$223$	4.49831	−	6.04228i	0.301229	−	0.404621i	0.926805	+	0.375542i	$0.122543\pi$
$224$	−12.9452	−	4.71166i	−0.864936	−	0.314811i
$225$	0.122904	−	13.7456i	0.00819361	−	0.916373i
$226$	−28.3955	+	10.3351i	−1.88884	+	0.687481i
$227$	3.91290	−	13.0700i	0.259708	−	0.867485i	−0.724319	−	0.689465i	$-0.757846\pi$
$227$	3.91290	−	13.0700i	0.259708	−	0.867485i	0.984027	−	0.178020i	$-0.0569692\pi$
$228$	21.2081	+	21.3986i	1.40454	+	1.41715i
$229$	−0.929998	+	15.9675i	−0.0614560	+	1.05516i	0.816785	+	0.576942i	$0.195754\pi$
$229$	−0.929998	+	15.9675i	−0.0614560	+	1.05516i	−0.878241	+	0.478218i	$0.841283\pi$
$230$	3.66280	+	2.40906i	0.241518	+	0.158849i
$231$	−3.46695	−	1.63558i	−0.228109	−	0.107613i
$232$	−9.14898	+	2.16835i	−0.600660	+	0.142359i
$233$	−0.930605	+	5.27772i	−0.0609660	+	0.345755i	0.939032	+	0.343829i	$0.111724\pi$
$233$	−0.930605	+	5.27772i	−0.0609660	+	0.345755i	−0.999998	+	0.00192589i	$0.999387\pi$
$234$	34.7353	+	2.33490i	2.27072	+	0.152637i
$235$	0.685064	+	3.88519i	0.0446886	+	0.253442i
$236$	2.26129	+	5.24226i	0.147197	+	0.341242i
$237$	24.6887	−	0.607917i	1.60371	−	0.0394884i
$238$	7.81658	+	26.1092i	0.506673	+	1.69241i
$239$	−9.64028	−	12.9491i	−0.623578	−	0.837611i	0.372319	−	0.928105i	$-0.378563\pi$
$239$	−9.64028	−	12.9491i	−0.623578	−	0.837611i	−0.995897	+	0.0904942i	$0.971155\pi$
$240$	1.96884	−	1.05025i	0.127088	−	0.0677935i
$241$	−20.9003	−	10.4965i	−1.34630	−	0.676139i	−0.377975	−	0.925816i	$-0.623379\pi$
$241$	−20.9003	−	10.4965i	−1.34630	−	0.676139i	−0.968329	+	0.249677i	$0.919676\pi$
$242$	−20.7491			−1.33380
$243$	12.0087	+	9.93940i	0.770357	+	0.637613i
$244$	−9.81564			−0.628382
$245$	−2.11074	−	1.06005i	−0.134850	−	0.0677243i
$246$	−3.70881	+	1.97842i	−0.236465	+	0.126140i
$247$	−20.2621	−	27.2168i	−1.28925	−	1.73176i
$248$	1.27051	+	4.24380i	0.0806774	+	0.269481i
$249$	−11.6349	+	0.286489i	−0.737333	+	0.0181555i
$250$	−5.33858	−	12.3762i	−0.337641	−	0.782740i
$251$	4.21745	+	23.9183i	0.266203	+	1.50971i	0.765588	+	0.643331i	$0.222448\pi$
$251$	4.21745	+	23.9183i	0.266203	+	1.50971i	−0.499385	+	0.866380i	$0.666441\pi$
$252$	−6.61406	−	13.4686i	−0.416646	−	0.848442i
$253$	0.654768	−	3.71337i	0.0411649	−	0.233458i
$254$	−24.1261	+	5.71800i	−1.51381	+	0.358779i
$255$	−6.93439	−	3.27138i	−0.434248	−	0.204862i
$256$	0.945527	+	0.621883i	0.0590954	+	0.0388677i
$257$	−0.560163	+	9.61763i	−0.0349420	+	0.599931i	0.934705	+	0.355423i	$0.115663\pi$
$257$	−0.560163	+	9.61763i	−0.0349420	+	0.599931i	−0.969647	+	0.244508i	$0.921374\pi$
$258$	−25.5589	−	25.7884i	−1.59123	−	1.60552i
$259$	−0.749638	+	2.50396i	−0.0465802	+	0.155589i
$260$	8.85887	−	3.22437i	0.549404	−	0.199967i
$261$	15.2136	+	8.96590i	0.941699	+	0.554975i
$262$	29.8116	+	10.8505i	1.84177	+	0.670349i
$263$	3.96621	−	5.32754i	0.244567	−	0.328510i	−0.662842	−	0.748759i	$-0.730650\pi$
$263$	3.96621	−	5.32754i	0.244567	−	0.328510i	0.907409	+	0.420249i	$0.138057\pi$
$264$	2.61629	+	2.08777i	0.161022	+	0.128494i
$265$	−5.36136	−	1.27067i	−0.329346	−	0.0780564i
$266$	−10.0296	+	23.2512i	−0.614954	+	1.42562i
$267$	16.6433	+	21.2434i	1.01855	+	1.30007i
$268$	−2.78637	+	1.83262i	−0.170205	+	0.111945i
$269$	−14.6832	−	25.4321i	−0.895251	−	1.55062i	−0.833494	−	0.552529i	$-0.813663\pi$
$269$	−14.6832	−	25.4321i	−0.895251	−	1.55062i	−0.0617568	−	0.998091i	$-0.519670\pi$
$270$	7.03408	+	1.98626i	0.428081	+	0.120880i
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	−0.422799	−	0.906223i	$-0.638952\pi$
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	0.996212	−	0.0869568i	$-0.0277142\pi$
$272$	0.793397	+	13.6221i	0.0481067	+	0.825961i
$273$	5.24376	+	16.0650i	0.317367	+	0.972296i
$274$	0.801351	−	0.0936645i	0.0484114	−	0.00565848i
$275$	−3.80421	+	4.03223i	−0.229403	+	0.243152i
$276$	11.0694	−	9.76261i	0.666300	−	0.587640i
$277$	−13.9438	−	1.62979i	−0.837801	−	0.0979249i	−0.313638	−	0.949543i	$-0.601548\pi$
$277$	−13.9438	−	1.62979i	−0.837801	−	0.0979249i	−0.524163	+	0.851618i	$0.675622\pi$
$278$	24.9640	−	20.9473i	1.49724	−	1.25633i
$279$	3.80032	−	7.40130i	0.227519	−	0.443104i
$280$	−1.44713	−	1.21428i	−0.0864824	−	0.0725673i
$281$	15.1525	+	16.0607i	0.903924	+	0.958103i	0.999303	−	0.0373380i	$-0.0118878\pi$
$281$	15.1525	+	16.0607i	0.903924	+	0.958103i	−0.0953791	+	0.995441i	$0.530406\pi$
$282$	22.9006	+	2.10675i	1.36371	+	0.125455i
$283$	3.53563	−	1.77566i	0.210172	−	0.105552i	−0.340599	−	0.940208i	$-0.610630\pi$
$283$	3.53563	−	1.77566i	0.210172	−	0.105552i	0.550771	+	0.834656i	$0.314334\pi$
$284$	19.9136	−	10.0010i	1.18166	−	0.593451i
$285$	−2.98175	−	6.46975i	−0.176624	−	0.383235i
$286$	−9.63461	−	10.2121i	−0.569707	−	0.603854i
$287$	−1.56307	−	1.31157i	−0.0922652	−	0.0774197i
$288$	−5.01325	−	22.0285i	−0.295409	−	1.29804i
$289$	22.8934	−	19.2099i	1.34667	−	1.12999i
$290$	8.22401	+	0.961249i	0.482931	+	0.0564465i
$291$	1.27790	+	6.33166i	0.0749116	+	0.371168i
$292$	−12.0502	+	12.7724i	−0.705183	+	0.747450i
$293$	−7.92333	+	0.926104i	−0.462886	+	0.0541036i	−0.344340	−	0.938845i	$-0.611897\pi$
$293$	−7.92333	+	0.926104i	−0.462886	+	0.0541036i	−0.118546	+	0.992949i	$0.537823\pi$
$294$	−9.19925	+	10.2445i	−0.536511	+	0.597473i
$295$	−0.0784927	−	1.34767i	−0.00457002	−	0.0784643i
$296$	1.14114	−	1.97650i	0.0663271	−	0.114882i
$297$	−0.827614	−	6.23180i	−0.0480231	−	0.361606i
$298$	1.08818	+	1.88478i	0.0630366	+	0.109183i
$299$	−13.8880	+	9.13425i	−0.803161	+	0.528247i
$300$	−21.4837	+	3.04886i	−1.24036	+	0.176026i
$301$	6.98076	−	16.1832i	0.402365	−	0.932786i
$302$	0.0415649	+	0.00985106i	0.00239179	+	0.000566865i
$303$	1.20305	−	7.96469i	0.0691134	−	0.457560i
$304$	−7.57072	+	10.1692i	−0.434211	+	0.583246i
$305$	2.18097	+	0.793808i	0.124882	+	0.0454533i
$306$	−29.0344	+	33.9802i	−1.65979	+	1.94252i
$307$	1.95823	−	0.712736i	0.111762	−	0.0406780i	−0.285534	−	0.958369i	$-0.592171\pi$
$307$	1.95823	−	0.712736i	0.111762	−	0.0406780i	0.397296	+	0.917691i	$0.369949\pi$
$308$	−1.73550	+	5.79699i	−0.0988895	+	0.330314i
$309$	−8.65735	+	2.27830i	−0.492500	+	0.129608i
$310$	0.226827	−	3.89447i	0.0128829	−	0.221191i
$311$	12.5444	+	8.25056i	0.711326	+	0.467846i	0.852895	−	0.522082i	$-0.174845\pi$
$311$	12.5444	+	8.25056i	0.711326	+	0.467846i	−0.141570	+	0.989928i	$0.545215\pi$
$312$	−1.22033	−	14.7053i	−0.0690874	−	0.832523i
$313$	4.95368	−	1.17404i	0.279998	−	0.0663608i	−0.0882173	−	0.996101i	$-0.528117\pi$
$313$	4.95368	−	1.17404i	0.279998	−	0.0663608i	0.368216	+	0.929740i	$0.379969\pi$
$314$	−2.94876	+	16.7232i	−0.166408	+	0.943747i
$315$	0.380370	+	3.52752i	0.0214314	+	0.198753i
$316$	−6.76955	−	38.3920i	−0.380817	−	2.15972i
$317$	−10.9746	−	25.4420i	−0.616396	−	1.42897i	−0.884943	−	0.465700i	$-0.845803\pi$
$317$	−10.9746	−	25.4420i	−0.616396	−	1.42897i	0.268547	−	0.963267i	$-0.413457\pi$
$318$	−15.3698	+	28.2025i	−0.861896	+	1.58152i
$319$	−2.04248	−	6.82236i	−0.114357	−	0.381979i
$320$	−4.78694	−	6.42998i	−0.267598	−	0.359447i
$321$	−19.0974	−	11.8976i	−1.06591	−	0.664061i
$322$	11.0857	+	5.56744i	0.617781	+	0.310261i
$323$	43.5617			2.42384
$324$	12.6827	−	21.0870i	0.704593	−	1.17150i
$325$	24.4382			1.35559
$326$	−29.9331	−	15.0330i	−1.65784	−	0.832599i
$327$	0.103293	−	3.07677i	0.00571212	−	0.170146i
$328$	1.06393	+	1.42911i	0.0587459	+	0.0789094i
$329$	3.20166	+	10.6943i	0.176513	+	0.589595i
$330$	−1.53621	−	2.51567i	−0.0845654	−	0.138483i
$331$	10.8007	+	25.0389i	0.593663	+	1.37626i	0.904774	+	0.425891i	$0.140039\pi$
$331$	10.8007	+	25.0389i	0.593663	+	1.37626i	−0.311112	+	0.950373i	$0.600701\pi$
$332$	3.19024	+	18.0928i	0.175087	+	0.992969i
$333$	−4.11717	+	1.19259i	−0.225620	+	0.0653538i
$334$	1.38088	−	7.83136i	0.0755584	−	0.428513i
$335$	0.767320	−	0.181858i	0.0419232	−	0.00993597i
$336$	5.18840	−	3.59850i	0.283050	−	0.196314i
$337$	10.6262	+	6.98897i	0.578846	+	0.380713i	0.804908	−	0.593400i	$-0.202215\pi$
$337$	10.6262	+	6.98897i	0.578846	+	0.380713i	−0.226062	+	0.974113i	$0.572585\pi$
$338$	−1.95408	+	33.5502i	−0.106288	+	1.82489i
$339$	6.32968	−	23.2072i	0.343781	−	1.26044i
$340$	−3.47125	+	11.5948i	−0.188255	+	0.628815i
$341$	−3.15292	+	1.14757i	−0.170740	+	0.0621444i
$342$	−40.9587	+	6.84511i	−2.21479	+	0.370141i
$343$	−18.3136	−	6.66560i	−0.988840	−	0.359908i
$344$	−9.18988	+	12.3441i	−0.495485	+	0.665552i
$345$	−3.24907	+	1.27398i	−0.174924	+	0.0685890i
$346$	28.1213	+	6.66487i	1.51181	+	0.358306i
$347$	3.33227	−	7.72507i	0.178886	−	0.414703i	−0.805055	−	0.593200i	$-0.797864\pi$
$347$	3.33227	−	7.72507i	0.178886	−	0.414703i	0.983940	+	0.178497i	$0.0571235\pi$
$348$	10.4076	−	25.8599i	0.557906	−	1.38624i
$349$	−25.1843	+	16.5640i	−1.34808	+	0.886649i	−0.998732	−	0.0503430i	$-0.983969\pi$
$349$	−25.1843	+	16.5640i	−1.34808	+	0.886649i	−0.349352	+	0.936992i	$0.613598\pi$
$350$	−9.11893	−	15.7944i	−0.487427	−	0.844249i
$351$	−17.4789	+	21.5064i	−0.932954	+	1.14793i
$352$	−4.55540	+	7.89018i	−0.242803	+	0.420548i
$353$	−1.35078	−	23.1921i	−0.0718950	−	1.23439i	−0.820606	−	0.571494i	$-0.806364\pi$
$353$	−1.35078	−	23.1921i	−0.0718950	−	1.23439i	0.748711	−	0.662896i	$-0.230673\pi$
$354$	−7.69951	−	1.62574i	−0.409224	−	0.0864073i
$355$	−5.23347	+	0.611705i	−0.277764	+	0.0324660i
$356$	29.2338	−	30.9860i	1.54939	−	1.64226i
$357$	−20.5637	−	6.91626i	−1.08835	−	0.366047i
$358$	−0.903214	−	0.105571i	−0.0477364	−	0.00557958i
$359$	3.19290	−	2.67916i	0.168515	−	0.141401i	−0.554630	−	0.832097i	$-0.687140\pi$
$359$	3.19290	−	2.67916i	0.168515	−	0.141401i	0.723145	+	0.690696i	$0.242696\pi$
$360$	0.387152	−	3.07370i	0.0204047	−	0.161998i
$361$	16.4498	+	13.8030i	0.865780	+	0.726476i
$362$	−31.1245	−	32.9901i	−1.63587	−	1.73392i
$363$	9.53435	−	13.4877i	0.500423	−	0.707922i
$364$	23.8387	−	11.9722i	1.24948	−	0.627515i
$365$	3.71039	−	1.86343i	0.194211	−	0.0975364i
$366$	7.80964	−	11.0479i	0.408217	−	0.577482i
$367$	8.04346	+	8.52557i	0.419865	+	0.445031i	0.902435	−	0.430826i	$-0.141778\pi$
$367$	8.04346	+	8.52557i	0.419865	+	0.445031i	−0.482569	+	0.875858i	$0.660296\pi$
$368$	4.75778	+	3.99225i	0.248016	+	0.208110i
$369$	0.418171	−	3.31997i	0.0217691	−	0.172831i
$370$	−1.53961	+	1.29189i	−0.0800407	+	0.0671621i
$371$	−15.4855	−	1.81000i	−0.803967	−	0.0939703i
$372$	−12.4483	−	4.18676i	−0.645412	−	0.217073i
$373$	−24.9598	+	26.4559i	−1.29237	+	1.36983i	−0.401313	+	0.915941i	$0.631446\pi$
$373$	−24.9598	+	26.4559i	−1.29237	+	1.36983i	−0.891057	+	0.453891i	$0.850036\pi$
$374$	17.9028	−	2.09253i	0.925729	−	0.108202i
$375$	10.4981	+	2.21667i	0.542121	+	0.114468i
$376$	−0.566763	−	9.73095i	−0.0292286	−	0.501835i
$377$	−15.6973	+	27.1885i	−0.808452	+	1.40028i
$378$	20.4218	+	3.27168i	1.05038	+	0.168277i
$379$	5.02516	+	8.70383i	0.258125	+	0.447086i	0.965740	−	0.259513i	$-0.0835620\pi$
$379$	5.02516	+	8.70383i	0.258125	+	0.447086i	−0.707615	+	0.706599i	$0.750229\pi$
$380$	−9.39529	+	6.17938i	−0.481968	+	0.316996i
$381$	7.36920	−	18.3104i	0.377535	−	0.938069i
$382$	5.93710	−	13.7637i	0.303768	−	0.704214i
$383$	−0.294453	−	0.0697866i	−0.0150458	−	0.00356593i	0.223086	−	0.974799i	$-0.428387\pi$
$383$	−0.294453	−	0.0697866i	−0.0150458	−	0.00356593i	−0.238132	+	0.971233i	$0.576535\pi$
$384$	−19.2176	+	7.53537i	−0.980694	+	0.384538i
$385$	0.854430	−	1.14770i	0.0435458	−	0.0584921i
$386$	17.8828	+	6.50880i	0.910209	+	0.331289i
$387$	28.5079	−	4.76431i	1.44914	−	0.242183i
$388$	9.58146	−	3.48737i	0.486425	−	0.177044i
$389$	−2.15663	+	7.20364i	−0.109345	+	0.365239i	−0.995095	−	0.0989244i	$-0.968460\pi$
$389$	−2.15663	+	7.20364i	−0.109345	+	0.365239i	0.885750	+	0.464164i	$0.153645\pi$
$390$	−3.41926	+	12.5364i	−0.173141	+	0.634806i
$391$	1.24085	−	21.3045i	0.0627524	−	1.07742i
$392$	4.87579	+	3.20686i	0.246265	+	0.161971i
$393$	−20.7519	+	14.3928i	−1.04679	+	0.726021i
$394$	−17.8841	+	4.23860i	−0.900987	+	0.213538i
$395$	−1.60068	+	9.07791i	−0.0805390	+	0.456759i
$396$	−9.53176	+	2.76100i	−0.478989	+	0.138746i
$397$	2.95983	+	16.7860i	0.148549	+	0.842466i	0.964448	+	0.264271i	$0.0851314\pi$
$397$	2.95983	+	16.7860i	0.148549	+	0.842466i	−0.815899	+	0.578195i	$0.803757\pi$
$398$	10.8763	+	25.2141i	0.545180	+	1.26387i
$399$	−10.5055	−	17.2037i	−0.525934	−	0.861263i
$400$	−2.61881	−	8.74745i	−0.130941	−	0.437372i
$401$	8.10789	+	10.8908i	0.404889	+	0.543860i	0.957067	−	0.289866i	$-0.0936108\pi$
$401$	8.10789	+	10.8908i	0.404889	+	0.543860i	−0.552179	+	0.833726i	$0.686203\pi$
$402$	0.154238	−	4.59426i	0.00769271	−	0.229141i
$403$	13.2181	+	6.63836i	0.658438	+	0.330680i
$404$	−12.7153			−0.632609
$405$	−4.52335	+	3.65973i	−0.224767	+	0.181853i
$406$	23.4293			1.16278
$407$	1.54476	+	0.775806i	0.0765708	+	0.0384553i
$408$	16.0790	+	10.0172i	0.796028	+	0.495924i
$409$	−0.401500	−	0.539308i	−0.0198529	−	0.0266671i	0.792086	−	0.610410i	$-0.208995\pi$
$409$	−0.401500	−	0.539308i	−0.0198529	−	0.0266671i	−0.811939	+	0.583743i	$0.801588\pi$
$410$	−0.449986	−	1.50306i	−0.0222232	−	0.0742308i
$411$	−0.307340	+	0.563948i	−0.0151600	+	0.0278175i
$412$	5.59715	+	12.9757i	0.275752	+	0.639265i
$413$	−0.663313	−	3.76184i	−0.0326395	−	0.185108i
$414$	2.18100	+	20.2265i	0.107191	+	0.994077i
$415$	0.754343	−	4.27809i	0.0370292	−	0.210003i
$416$	39.0814	−	9.26246i	1.91612	−	0.454130i
$417$	2.14542	+	25.8530i	0.105062	+	1.26602i
$418$	13.9918	+	9.20258i	0.684363	+	0.450113i
$419$	1.15627	−	19.8524i	0.0564876	−	0.969855i	−0.844376	−	0.535752i	$-0.820028\pi$
$419$	1.15627	−	19.8524i	0.0564876	−	0.969855i	0.900863	−	0.434103i	$-0.142935\pi$
$420$	5.41624	−	1.42536i	0.264285	−	0.0695503i
$421$	−3.60098	+	12.0281i	−0.175501	+	0.586214i	0.824298	+	0.566156i	$0.191570\pi$
$421$	−3.60098	+	12.0281i	−0.175501	+	0.586214i	−0.999799	+	0.0200574i	$0.993615\pi$
$422$	11.6049	−	4.22384i	0.564918	−	0.205613i
$423$	−11.8924	+	13.9182i	−0.578231	+	0.676727i
$424$	12.7926	+	4.65611i	0.621262	+	0.226121i
$425$	−18.7356	+	25.1663i	−0.908809	+	1.22074i
$426$	−4.58743	+	30.3707i	−0.222262	+	1.47146i
$427$	6.39038	+	1.51455i	0.309252	+	0.0732941i
$428$	−14.0679	+	32.6131i	−0.679999	+	1.57641i
$429$	11.0654	−	1.57035i	0.534243	−	0.0758171i
$430$	11.3227	−	7.44707i	0.546030	−	0.359130i
$431$	10.8013	+	18.7084i	0.520281	+	0.901153i	0.999722	+	0.0235787i	$0.00750603\pi$
$431$	10.8013	+	18.7084i	0.520281	+	0.901153i	−0.479441	+	0.877574i	$0.659161\pi$
$432$	9.57110	+	3.95178i	0.460490	+	0.190130i
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	−0.910067	−	0.414461i	$-0.863970\pi$
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	0.813968	+	0.580910i	$0.197303\pi$
$434$	−0.641838	−	11.0199i	−0.0308092	−	0.528973i
$435$	−4.40383	+	4.90422i	−0.211148	+	0.235140i
$436$	−4.82671	+	0.564162i	−0.231158	+	0.0270184i
$437$	13.6067	−	14.4223i	0.650897	−	0.689910i
$438$	−4.78835	−	23.7251i	−0.228796	−	1.13363i
$439$	31.0001	+	3.62339i	1.47955	+	0.172935i	0.817243	−	0.576293i	$-0.195501\pi$
$439$	31.0001	+	3.62339i	1.47955	+	0.172935i	0.662312	+	0.749228i	$0.269575\pi$
$440$	−0.957063	+	0.803071i	−0.0456262	+	0.0382849i
$441$	−2.43222	−	10.6873i	−0.115820	−	0.508918i
$442$	−60.8697	−	51.0758i	−2.89528	−	2.42943i
$443$	−1.09948	−	1.16538i	−0.0522379	−	0.0553689i	0.700728	−	0.713429i	$-0.252859\pi$
$443$	−1.09948	−	1.16538i	−0.0522379	−	0.0553689i	−0.752966	+	0.658060i	$0.771377\pi$
$444$	2.83213	+	6.14510i	0.134407	+	0.291634i
$445$	−9.00144	+	4.52070i	−0.426709	+	0.214302i
$446$	14.6467	−	7.35584i	0.693540	−	0.348309i
$447$	−1.72521	−	0.158711i	−0.0815995	−	0.00750677i
$448$	−15.5659	−	16.4989i	−0.735421	−	0.779501i
$449$	8.04720	+	6.75241i	0.379771	+	0.318666i	0.812613	−	0.582804i	$-0.198045\pi$
$449$	8.04720	+	6.75241i	0.379771	+	0.318666i	−0.432841	+	0.901470i	$0.642489\pi$
$450$	13.6615	−	26.6065i	0.644011	−	1.25424i
$451$	−1.03374	+	0.867414i	−0.0486771	+	0.0408449i
$452$	−37.7152	−	4.40827i	−1.77397	−	0.207348i
$453$	−0.0255029	+	0.0224921i	−0.00119823	+	0.00105677i
$454$	20.3710	−	21.5920i	0.956057	−	1.01336i
$455$	−6.26500	+	0.732273i	−0.293708	+	0.0343295i
$456$	5.46160	+	16.7324i	0.255763	+	0.783564i
$457$	−2.39213	−	41.0713i	−0.111899	−	1.92123i	−0.327676	−	0.944790i	$-0.606265\pi$
$457$	−2.39213	−	41.0713i	−0.111899	−	1.92123i	0.215777	−	0.976443i	$-0.430772\pi$
$458$	−17.4005	+	30.1385i	−0.813071	+	1.40828i
$459$	−8.74692	−	34.4876i	−0.408271	−	1.60974i
$460$	2.75450	+	4.77093i	0.128429	+	0.222446i
$461$	28.6563	−	18.8476i	1.33466	−	0.877819i	0.336696	−	0.941613i	$-0.390691\pi$
$461$	28.6563	−	18.8476i	1.33466	−	0.877819i	0.997963	+	0.0637944i	$0.0203202\pi$
$462$	−5.14390	−	6.56565i	−0.239316	−	0.305462i
$463$	−13.2025	+	30.6068i	−0.613572	+	1.42242i	0.273990	+	0.961732i	$0.411656\pi$
$463$	−13.2025	+	30.6068i	−0.613572	+	1.42242i	−0.887562	+	0.460688i	$0.847603\pi$
$464$	11.4140	+	2.70518i	0.529884	+	0.125585i
$465$	2.42733	+	1.93698i	0.112565	+	0.0898254i
$466$	−6.96314	+	9.35312i	−0.322561	+	0.433275i
$467$	−9.76380	−	3.55373i	−0.451815	−	0.164447i	0.106082	−	0.994357i	$-0.466169\pi$
$467$	−9.76380	−	3.55373i	−0.451815	−	0.164447i	−0.557897	+	0.829910i	$0.688392\pi$
$468$	37.6891	+	22.2114i	1.74218	+	1.02672i
$469$	2.09681	−	0.763177i	0.0968218	−	0.0352402i
$470$	−2.46187	+	8.22322i	−0.113558	+	0.379309i
$471$	−9.51578	−	9.60124i	−0.438464	−	0.442402i
$472$	−0.193936	+	3.32976i	−0.00892664	+	0.153265i
$473$	−9.73855	−	6.40515i	−0.447779	−	0.294509i
$474$	48.5977	+	22.9265i	2.23217	+	1.05305i
$475$	−28.3647	+	6.72257i	−1.30146	+	0.308453i
$476$	−5.94706	+	33.7274i	−0.272583	+	1.54589i
$477$	−11.2702	−	22.9502i	−0.516027	−	1.05082i
$478$	−6.09945	−	34.5917i	−0.278982	−	1.58219i
$479$	8.03903	+	18.6366i	0.367313	+	0.851526i	0.997196	+	0.0748364i	$0.0238435\pi$
$479$	8.03903	+	18.6366i	0.367313	+	0.851526i	−0.629883	+	0.776690i	$0.716897\pi$
$480$	8.42988	−	0.207571i	0.384770	−	0.00947428i
$481$	−2.18558	−	7.30034i	−0.0996538	−	0.332867i
$482$	−30.3880	−	40.8182i	−1.38414	−	1.85922i
$483$	−8.71299	+	4.64785i	−0.396455	+	0.211484i
$484$	−23.3001	−	11.7017i	−1.05910	−	0.531898i
$485$	−2.41096			−0.109476
$486$	13.6435	+	31.0524i	0.618882	+	1.40856i
$487$	−27.5716			−1.24939			−0.624694	−	0.780870i	$-0.714776\pi$
$487$	−27.5716			−1.24939			−0.624694	+	0.780870i	$0.714776\pi$
$488$	−5.12451	−	2.57363i	−0.231976	−	0.116503i
$489$	23.5264	−	12.5499i	1.06390	−	0.567527i
$490$	−3.06892	−	4.12227i	−0.138640	−	0.186225i
$491$	−2.93035	−	9.78804i	−0.132245	−	0.441728i	0.866059	−	0.499941i	$-0.166645\pi$
$491$	−2.93035	−	9.78804i	−0.132245	−	0.441728i	−0.998304	+	0.0582128i	$0.981460\pi$
$492$	−5.28055	+	0.130024i	−0.238066	+	0.00586194i
$493$	−15.9642	−	37.0091i	−0.718991	−	1.66681i
$494$	−12.8199	−	72.7055i	−0.576796	−	3.27117i
$495$	2.34118	+	0.157373i	0.105228	+	0.00707341i
$496$	0.959690	−	5.44267i	0.0430914	−	0.244383i
$497$	−14.5077	+	3.43840i	−0.650761	+	0.154233i
$498$	−22.9023	−	10.8044i	−1.02628	−	0.484159i
$499$	7.30520	+	4.80470i	0.327026	+	0.215088i	0.702395	−	0.711787i	$-0.252114\pi$
$499$	7.30520	+	4.80470i	0.327026	+	0.215088i	−0.375370	+	0.926875i	$0.622484\pi$
$500$	0.984811	−	16.9086i	0.0440421	−	0.756174i
$501$	4.45616	+	4.49618i	0.199087	+	0.200875i
$502$	−15.1560	+	50.6244i	−0.676444	+	2.25948i
$503$	−12.2947	+	4.47489i	−0.548192	+	0.199526i	−0.601243	−	0.799066i	$-0.705328\pi$
$503$	−12.2947	+	4.47489i	−0.548192	+	0.199526i	0.0530509	+	0.998592i	$0.483105\pi$
$504$	0.0783782	−	8.76581i	0.00349124	−	0.390460i
$505$	2.82525	+	1.02831i	0.125722	+	0.0457591i
$506$	4.89922	−	6.58080i	0.217797	−	0.292552i
$507$	−20.9110	−	16.6868i	−0.928690	−	0.741085i
$508$	−30.3171	−	7.18528i	−1.34510	−	0.318795i
$509$	−12.0492	+	27.9331i	−0.534070	+	1.23811i	0.411117	+	0.911583i	$0.365139\pi$
$509$	−12.0492	+	27.9331i	−0.534070	+	1.23811i	−0.945187	+	0.326530i	$0.894120\pi$
$510$	−10.2885	−	13.1322i	−0.455584	−	0.581504i
$511$	9.81592	−	6.45603i	0.434231	−	0.285598i
$512$	−10.6866	−	18.5097i	−0.472284	−	0.818019i
$513$	14.3712	−	29.7701i	0.634504	−	1.31438i
$514$	−10.4808	+	18.1532i	−0.462287	+	0.800705i
$515$	−0.194286	−	3.33575i	−0.00856124	−	0.146991i
$516$	−14.1575	−	43.3732i	−0.623247	−	1.90940i
$517$	7.33294	−	0.857098i	0.322502	−	0.0376951i
$518$	−3.90269	+	4.13661i	−0.171475	+	0.181752i
$519$	−17.2543	+	15.2174i	−0.757382	+	0.667969i
$520$	5.47042	+	0.639401i	0.239894	+	0.0280396i
$521$	8.25925	−	6.93034i	0.361845	−	0.303624i	−0.443681	−	0.896185i	$-0.646328\pi$
$521$	8.25925	−	6.93034i	0.361845	−	0.303624i	0.805525	+	0.592561i	$0.201883\pi$
$522$	20.8257	+	32.2891i	0.911517	+	1.41326i
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	0.825517	−	0.564377i	$-0.190884\pi$
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	−0.412453	+	0.910979i	$0.635328\pi$
$524$	27.3575	+	28.9972i	1.19512	+	1.26675i
$525$	14.4572	+	1.32999i	0.630964	+	0.0580457i
$526$	12.9141	−	6.48572i	0.563083	−	0.282791i
$527$	−16.9698	+	8.52256i	−0.739216	+	0.371248i
$528$	−1.74787	−	3.79250i	−0.0760664	−	0.165047i
$529$	9.11771	+	9.66421i	0.396422	+	0.420183i
$530$	−9.18367	−	7.70601i	−0.398913	−	0.334728i
$531$	4.59477	−	4.25794i	0.199396	−	0.184779i
$532$	−24.3755	+	20.4535i	−1.05681	+	0.886772i
$533$	5.90872	+	0.690630i	0.255935	+	0.0299145i
$534$	11.6166	+	57.5572i	0.502698	+	2.49074i
$535$	5.76327	−	6.10871i	0.249168	−	0.264103i
$536$	−1.93520	+	0.226193i	−0.0835881	+	0.00977005i
$537$	0.483658	−	0.538614i	0.0208714	−	0.0232429i
$538$	−3.71520	−	63.7875i	−0.160174	−	2.75007i
$539$	−2.21009	+	3.82798i	−0.0951952	+	0.164883i
$540$	6.77870	+	6.19743i	0.291709	+	0.266695i
$541$	7.99279	+	13.8439i	0.343637	+	0.595196i	0.985105	−	0.171953i	$-0.0550078\pi$
$541$	7.99279	+	13.8439i	0.343637	+	0.595196i	−0.641468	+	0.767149i	$0.721674\pi$
$542$	34.3196	−	22.5724i	1.47415	−	0.969566i
$543$	35.7467	−	5.07299i	1.53404	−	0.217703i
$544$	−20.4234	+	47.3469i	−0.875648	+	2.02998i
$545$	1.11809	+	0.264991i	0.0478936	+	0.0113510i
$546$	−5.49162	+	36.3568i	−0.235019	+	1.55593i
$547$	0.738452	−	0.991913i	0.0315739	−	0.0424111i	−0.786056	−	0.618155i	$-0.787880\pi$
$547$	0.738452	−	0.991913i	0.0315739	−	0.0424111i	0.817630	+	0.575744i	$0.195288\pi$
$548$	0.952696	+	0.346753i	0.0406972	+	0.0148126i
$549$	3.59296	+	10.1531i	0.153344	+	0.433325i
$550$	−11.3343	+	4.12534i	−0.483295	+	0.175905i
$551$	10.7403	−	35.8751i	0.457552	−	1.52833i
$552$	8.33879	−	2.19446i	0.354923	−	0.0934026i
$553$	−1.51662	+	26.0393i	−0.0644930	+	1.10730i
$554$	−25.5204	−	16.7850i	−1.08426	−	0.713128i
$555$	−0.132315	−	1.59444i	−0.00561648	−	0.0676801i
$556$	39.8467	−	9.44384i	1.68988	−	0.400508i
$557$	2.28246	−	12.9445i	0.0967109	−	0.548475i	−0.897499	−	0.441017i	$-0.854618\pi$
$557$	2.28246	−	12.9445i	0.0967109	−	0.548475i	0.994210	−	0.107458i	$-0.0342710\pi$
$558$	14.6166	−	10.6799i	0.618770	−	0.452115i
$559$	8.92289	+	50.6042i	0.377398	+	2.14033i
$560$	0.933474	+	2.16404i	0.0394465	+	0.0914472i
$561$	−6.86620	+	12.5990i	−0.289891	+	0.531931i
$562$	13.7788	+	46.0245i	0.581224	+	1.94142i
$563$	3.63605	+	4.88406i	0.153241	+	0.205838i	0.872114	−	0.489303i	$-0.162749\pi$
$563$	3.63605	+	4.88406i	0.153241	+	0.205838i	−0.718873	+	0.695142i	$0.755342\pi$
$564$	24.5280	+	15.2809i	1.03281	+	0.643441i
$565$	8.02355	+	4.02958i	0.337553	+	0.169526i
$566$	8.60852			0.361843
$567$	−11.5106	+	11.7716i	−0.483402	+	0.494360i
$568$	13.0187			0.546251
$569$	14.8144	+	7.44006i	0.621051	+	0.311904i	0.731358	−	0.681994i	$-0.238887\pi$
$569$	14.8144	+	7.44006i	0.621051	+	0.311904i	−0.110307	+	0.993898i	$0.535183\pi$
$570$	0.520073	−	15.4913i	0.0217834	−	0.648858i
$571$	20.8094	+	27.9518i	0.870844	+	1.16975i	0.984353	+	0.176210i	$0.0563838\pi$
$571$	20.8094	+	27.9518i	0.870844	+	1.16975i	−0.113508	+	0.993537i	$0.536209\pi$
$572$	−5.05988	−	16.9012i	−0.211564	−	0.706674i
$573$	6.21882	+	10.1839i	0.259795	+	0.425437i
$574$	−1.75844	−	4.07652i	−0.0733959	−	0.170151i
$575$	2.47981	+	14.0637i	0.103415	+	0.586497i
$576$	8.90184	−	36.1176i	0.370910	−	1.50490i
$577$	5.38675	−	30.5498i	0.224254	−	1.27180i	−0.639854	−	0.768497i	$-0.721005\pi$
$577$	5.38675	−	30.5498i	0.224254	−	1.27180i	0.864107	−	0.503308i	$-0.167884\pi$
$578$	63.2718	−	14.9957i	2.63176	−	0.623739i
$579$	−12.4482	+	8.63366i	−0.517330	+	0.358802i
$580$	8.69300	+	5.71747i	0.360957	+	0.237405i
$581$	0.714726	−	12.2714i	0.0296518	−	0.509102i
$582$	−3.69816	+	13.5590i	−0.153294	+	0.562037i
$583$	−2.95726	+	9.87794i	−0.122477	+	0.409103i
$584$	−9.63999	+	3.50867i	−0.398906	+	0.145190i
$585$	−6.57797	−	7.98321i	−0.271966	−	0.330065i
$586$	−16.3102	−	5.93644i	−0.673769	−	0.245232i
$587$	−26.6000	+	35.7300i	−1.09790	+	1.47474i	−0.233214	+	0.972425i	$0.574924\pi$
$587$	−26.6000	+	35.7300i	−1.09790	+	1.47474i	−0.864687	+	0.502311i	$0.832483\pi$
$588$	−16.1078	+	6.31598i	−0.664274	+	0.260467i
$589$	−17.1680	−	4.06889i	−0.707394	−	0.167655i
$590$	1.16338	−	2.69702i	0.0478956	−	0.111034i
$591$	5.46259	−	13.5730i	0.224701	−	0.558319i
$592$	−2.37889	+	1.56462i	−0.0977718	+	0.0643055i
$593$	9.90549	+	17.1568i	0.406770	+	0.704546i	0.994526	−	0.104493i	$-0.0333219\pi$
$593$	9.90549	+	17.1568i	0.406770	+	0.704546i	−0.587756	+	0.809038i	$0.699989\pi$
$594$	4.47616	−	12.9251i	0.183659	−	0.530323i
$595$	4.04899	−	7.01306i	0.165992	−	0.287507i
$596$	0.159016	+	2.73020i	0.00651356	+	0.111833i
$597$	−21.3879	−	4.51602i	−0.875347	−	0.184828i
$598$	−35.9229	+	4.19879i	−1.46900	+	0.171701i
$599$	19.1656	−	20.3143i	0.783084	−	0.830020i	−0.205818	−	0.978590i	$-0.565986\pi$
$599$	19.1656	−	20.3143i	0.783084	−	0.830020i	0.988902	+	0.148570i	$0.0474671\pi$
$600$	−12.0155	−	4.04122i	−0.490532	−	0.164982i
$601$	10.0762	+	1.17774i	0.411015	+	0.0480408i	0.319088	−	0.947725i	$-0.396623\pi$
$601$	10.0762	+	1.17774i	0.411015	+	0.0480408i	0.0919270	+	0.995766i	$0.470697\pi$
$602$	29.3761	−	24.6495i	1.19728	−	1.00464i
$603$	2.91557	+	2.21135i	0.118731	+	0.0900532i
$604$	0.0411194	+	0.0345033i	0.00167313	+	0.00140392i
$605$	4.23078	+	4.48437i	0.172006	+	0.182315i
$606$	10.1167	−	14.3115i	0.410963	−	0.581366i
$607$	9.66590	−	4.85440i	0.392327	−	0.197034i	−0.241690	−	0.970354i	$-0.577702\pi$
$607$	9.66590	−	4.85440i	0.392327	−	0.197034i	0.634016	+	0.773320i	$0.281405\pi$
$608$	−42.8128	+	21.5014i	−1.73629	+	0.871997i
$609$	−10.7659	+	15.2300i	−0.436258	+	0.617150i
$610$	3.46546	+	3.67317i	0.140312	+	0.148722i
$611$	−24.9321	−	20.9205i	−1.00865	−	0.846355i
$612$	−51.7676	+	21.7835i	−2.09258	+	0.880545i
$613$	4.13859	−	3.47269i	0.167156	−	0.140261i	−0.555372	−	0.831602i	$-0.687424\pi$
$613$	4.13859	−	3.47269i	0.167156	−	0.140261i	0.722528	+	0.691341i	$0.242980\pi$
$614$	4.50351	+	0.526385i	0.181747	+	0.0212432i
$615$	1.18382	+	0.398156i	0.0477361	+	0.0160552i
$616$	−2.42601	+	2.57143i	−0.0977469	+	0.103606i
$617$	24.8710	−	2.90700i	1.00127	−	0.117031i	0.400367	−	0.916355i	$-0.368883\pi$
$617$	24.8710	−	2.90700i	1.00127	−	0.117031i	0.600901	+	0.799324i	$0.294809\pi$
$618$	−19.0579	−	4.02405i	−0.766620	−	0.161871i
$619$	−1.48183	−	25.4420i	−0.0595596	−	1.02260i	−0.887213	−	0.461360i	$-0.847362\pi$
$619$	−1.48183	−	25.4420i	−0.0595596	−	1.02260i	0.827654	−	0.561239i	$-0.189675\pi$
$620$	2.45106	−	4.24535i	0.0984368	−	0.170498i
$621$	−14.1502	−	7.87646i	−0.567827	−	0.316071i
$622$	16.3342	+	28.2917i	0.654943	+	1.13439i
$623$	−23.8135	+	15.6624i	−0.954068	+	0.627500i
$624$	−6.87314	+	17.0778i	−0.275146	+	0.683660i
$625$	7.48804	−	17.3592i	0.299521	−	0.694369i
$626$	10.7782	+	2.55449i	0.430785	+	0.102098i
$627$	−12.4114	+	4.86659i	−0.495662	+	0.194353i
$628$	−12.7426	+	17.1163i	−0.508485	+	0.683014i
$629$	9.19342	+	3.34613i	0.366566	+	0.133419i
$630$	−2.70504	+	7.23024i	−0.107772	+	0.288060i
$631$	−18.7709	+	6.83203i	−0.747256	+	0.271979i	−0.687451	−	0.726231i	$-0.741270\pi$
$631$	−18.7709	+	6.83203i	−0.747256	+	0.271979i	−0.0598054	+	0.998210i	$0.519048\pi$
$632$	6.53203	−	21.8185i	0.259830	−	0.867893i
$633$	−2.58687	+	9.48451i	−0.102819	+	0.376976i
$634$	3.50540	−	60.1854i	0.139217	−	2.39027i
$635$	6.15516	+	4.04831i	0.244260	+	0.160652i
$636$	−33.1646	+	23.0019i	−1.31506	+	0.912083i
$637$	18.9606	−	4.49376i	0.751248	−	0.178049i
$638$	2.69069	−	15.2597i	0.106526	−	0.604137i
$639$	−17.6342	−	16.9375i	−0.697596	−	0.670038i
$640$	−1.33792	−	7.58769i	−0.0528857	−	0.299930i
$641$	−3.53682	−	8.19927i	−0.139696	−	0.323852i	0.833978	−	0.551798i	$-0.186058\pi$
$641$	−3.53682	−	8.19927i	−0.139696	−	0.323852i	−0.973674	+	0.227947i	$0.926799\pi$
$642$	−25.5144	−	41.7820i	−1.00697	−	1.64900i
$643$	−3.84314	−	12.8370i	−0.151559	−	0.506241i	0.848165	−	0.529731i	$-0.177707\pi$
$643$	−3.84314	−	12.8370i	−0.151559	−	0.506241i	−0.999724	+	0.0234904i	$0.992522\pi$
$644$	9.30877	+	12.5039i	0.366817	+	0.492721i
$645$	−0.361979	+	10.7822i	−0.0142529	+	0.424548i
$646$	84.7001	+	42.5380i	3.33248	+	1.67363i
$647$	−48.7223			−1.91547			−0.957736	−	0.287649i	$-0.907126\pi$
$647$	−48.7223			−1.91547			−0.957736	+	0.287649i	$0.907126\pi$
$648$	12.1503	−	7.68368i	0.477308	−	0.301843i
$649$	−2.52628			−0.0991653
$650$	47.5169	+	23.8639i	1.86376	+	0.936018i
$651$	7.45830	+	4.64651i	0.292314	+	0.182111i
$652$	−25.1351	−	33.7624i	−0.984368	−	1.32224i
$653$	−1.37807	−	4.60307i	−0.0539280	−	0.180132i	0.926782	−	0.375599i	$-0.122563\pi$
$653$	−1.37807	−	4.60307i	−0.0539280	−	0.180132i	−0.980710	+	0.195467i	$0.937378\pi$
$654$	3.20530	−	5.88151i	0.125337	−	0.229985i
$655$	−3.73359	−	8.65544i	−0.145883	−	0.338196i
$656$	−0.385978	−	2.18899i	−0.0150699	−	0.0854656i
$657$	17.6225	+	7.78921i	0.687519	+	0.303886i
$658$	−4.21775	+	23.9201i	−0.164425	+	0.932501i
$659$	−24.6111	+	5.83293i	−0.958712	+	0.227219i	−0.680046	−	0.733169i	$-0.738040\pi$
$659$	−24.6111	+	5.83293i	−0.958712	+	0.227219i	−0.278666	+	0.960388i	$0.589892\pi$
$660$	−0.306327	−	3.69132i	−0.0119238	−	0.143685i
$661$	11.8107	+	7.76805i	0.459385	+	0.302142i	0.758027	−	0.652223i	$-0.226163\pi$
$661$	11.8107	+	7.76805i	0.459385	+	0.302142i	−0.298642	+	0.954365i	$0.596534\pi$
$662$	−3.44987	+	59.2319i	−0.134083	+	2.30211i
$663$	61.1712	−	16.0980i	2.37569	−	0.625196i
$664$	−3.07831	+	10.2823i	−0.119462	+	0.399029i
$665$	7.07019	−	2.57334i	0.274170	−	0.0997898i
$666$	−9.16987	−	1.70157i	−0.355325	−	0.0659345i
$667$	−17.2393	−	6.27461i	−0.667510	−	0.242954i
$668$	5.96725	−	8.01541i	0.230880	−	0.310126i
$669$	−1.94866	+	12.9010i	−0.0753396	+	0.498780i
$670$	1.66954	+	0.395688i	0.0644999	+	0.0152868i
$671$	1.72032	−	3.98816i	0.0664123	−	0.153961i
$672$	23.6240	−	3.35260i	0.911315	−	0.129329i
$673$	−2.22854	+	1.46573i	−0.0859039	+	0.0564999i	−0.591734	−	0.806133i	$-0.701557\pi$
$673$	−2.22854	+	1.46573i	−0.0859039	+	0.0564999i	0.505830	+	0.862633i	$0.331186\pi$
$674$	13.8366	+	23.9656i	0.532965	+	0.923122i
$675$	11.0177	+	21.1064i	0.424071	+	0.812385i
$676$	−21.1154	+	36.5730i	−0.812131	+	1.40665i
$677$	0.858366	+	14.7376i	0.0329897	+	0.566411i	0.973790	+	0.227449i	$0.0730386\pi$
$677$	0.858366	+	14.7376i	0.0329897	+	0.566411i	−0.940800	+	0.338962i	$0.889924\pi$
$678$	34.9691	−	38.9425i	1.34298	−	1.49558i
$679$	−6.77601	+	0.792002i	−0.260040	+	0.0303943i
$680$	−4.85237	+	5.14321i	−0.186080	+	0.197233i
$681$	4.67502	+	23.1635i	0.179147	+	0.887629i
$682$	−7.25106	−	0.847527i	−0.277657	−	0.0324535i
$683$	−16.0712	+	13.4854i	−0.614948	+	0.516003i	−0.896211	−	0.443628i	$-0.853691\pi$
$683$	−16.0712	+	13.4854i	−0.614948	+	0.516003i	0.281263	+	0.959631i	$0.409247\pi$
$684$	−49.8547	−	15.4126i	−1.90624	−	0.589314i
$685$	−0.183640	−	0.154092i	−0.00701653	−	0.00588756i
$686$	−29.0994	−	30.8436i	−1.11102	−	1.17761i
$687$	−11.5956	−	25.1598i	−0.442398	−	0.959907i
$688$	17.1572	−	8.61667i	0.654112	−	0.328507i
$689$	40.6205	−	20.4004i	1.54752	−	0.777194i
$690$	−7.56143	−	0.695616i	−0.287859	−	0.0264816i
$691$	−23.9044	−	25.3372i	−0.909366	−	0.963872i	0.0901196	−	0.995931i	$-0.471275\pi$
$691$	−23.9044	−	25.3372i	−0.909366	−	0.963872i	−0.999486	+	0.0320589i	$0.989794\pi$
$692$	27.8199	+	23.3437i	1.05755	+	0.887394i
$693$	6.63158	−	0.326780i	0.251913	−	0.0124133i
$694$	14.0227	−	11.7664i	0.532294	−	0.446648i
$695$	−9.61740	−	1.12411i	−0.364809	−	0.0426400i
$696$	12.2139	−	10.7720i	0.462968	−	0.408312i
$697$	−5.24114	+	5.55529i	−0.198522	+	0.210421i
$698$	−65.1423	+	7.61404i	−2.46567	+	0.288196i
$699$	−2.88028	−	8.82412i	−0.108942	−	0.333759i
$700$	−1.33255	−	22.8790i	−0.0503657	−	0.864746i
$701$	21.8053	−	37.7679i	0.823576	−	1.42647i	−0.0794276	−	0.996841i	$-0.525309\pi$
$701$	21.8053	−	37.7679i	0.823576	−	1.42647i	0.903003	−	0.429634i	$-0.141357\pi$
$702$	−54.9864	+	24.7483i	−2.07533	+	0.934065i
$703$	4.54496	+	7.87209i	0.171416	+	0.296902i
$704$	−12.5335	+	8.24341i	−0.472374	+	0.310685i
$705$	−4.21416	−	5.37893i	−0.158715	−	0.202582i
$706$	20.0206	−	46.4130i	0.753487	−	1.74678i
$707$	8.27816	+	1.96196i	0.311332	+	0.0737871i
$708$	−7.72926	−	6.16787i	−0.290484	−	0.231803i
$709$	10.9085	−	14.6527i	0.409677	−	0.550292i	−0.548617	−	0.836074i	$-0.684846\pi$
$709$	10.9085	−	14.6527i	0.409677	−	0.550292i	0.958295	+	0.285781i	$0.0922530\pi$
$710$	−10.7731	−	3.92111i	−0.404309	−	0.147156i
$711$	−37.2341	+	21.0555i	−1.39639	+	0.789643i
$712$	23.3867	−	8.51206i	0.876453	−	0.319003i
$713$	−2.47898	+	8.28037i	−0.0928385	+	0.310102i
$714$	−33.2298	−	33.5283i	−1.24359	−	1.25476i
$715$	−0.242556	+	4.16453i	−0.00907109	+	0.155745i
$716$	−0.954722	−	0.627930i	−0.0356796	−	0.0234669i
$717$	25.2887	+	11.9302i	0.944422	+	0.445542i
$718$	8.82440	−	2.09142i	0.329324	−	0.0780511i
$719$	−3.15002	+	17.8647i	−0.117476	+	0.666240i	0.868018	+	0.496532i	$0.165393\pi$
$719$	−3.15002	+	17.8647i	−0.117476	+	0.666240i	−0.985494	+	0.169708i	$0.945718\pi$
$720$	−2.15263	+	3.21002i	−0.0802236	+	0.119630i
$721$	−1.64184	−	9.31131i	−0.0611451	−	0.346771i
$722$	18.5059	+	42.9015i	0.688718	+	1.59663i
$723$	40.4969	−	0.997164i	1.50610	−	0.0370849i
$724$	−16.3459	−	54.5991i	−0.607491	−	2.02916i
$725$	16.1063	+	21.6345i	0.598172	+	0.803484i
$726$	31.7091	−	16.9148i	1.17683	−	0.627769i
$727$	18.0996	+	9.08994i	0.671276	+	0.337127i	0.751579	−	0.659643i	$-0.229293\pi$
$727$	18.0996	+	9.08994i	0.671276	+	0.337127i	−0.0803032	+	0.996770i	$0.525589\pi$
$728$	15.5847			0.577606
$729$	−26.4545	−	5.39996i	−0.979796	−	0.199998i
$730$	9.03402			0.334364
$731$	−58.9526	−	29.6071i	−2.18044	−	1.09506i
$732$	15.0004	−	8.00179i	0.554431	−	0.295755i
$733$	−1.05577	−	1.41814i	−0.0389957	−	0.0523803i	0.782198	−	0.623030i	$-0.214099\pi$
$733$	−1.05577	−	1.41814i	−0.0389957	−	0.0523803i	−0.821193	+	0.570650i	$0.806691\pi$
$734$	7.31426	+	24.4313i	0.269974	+	0.901776i
$735$	4.08982	−	0.100705i	0.150855	−	0.00371455i
$736$	9.29608	+	21.5507i	0.342658	+	0.794371i
$737$	−0.256258	−	1.45331i	−0.00943939	−	0.0535334i
$738$	4.05503	−	6.04691i	0.149268	−	0.222590i
$739$	−1.58340	+	8.97988i	−0.0582461	+	0.330330i	−0.999982	−	0.00602346i	$-0.998083\pi$
$739$	−1.58340	+	8.97988i	−0.0582461	+	0.330330i	0.941736	+	0.336354i	$0.109194\pi$
$740$	−2.45748	+	0.582433i	−0.0903387	+	0.0214107i
$741$	53.1522	+	25.0752i	1.95260	+	0.921160i
$742$	−28.3421	−	18.6409i	−1.04047	−	0.684329i
$743$	1.15833	−	19.8878i	0.0424951	−	0.729613i	−0.908018	−	0.418930i	$-0.862405\pi$
$743$	1.15833	−	19.8878i	0.0424951	−	0.729613i	0.950514	−	0.310683i	$-0.100558\pi$
$744$	−5.40118	−	5.44969i	−0.198017	−	0.199795i
$745$	0.185464	−	0.619492i	0.00679487	−	0.0226964i
$746$	−74.3653	+	27.0667i	−2.72271	+	0.990984i
$747$	17.5471	−	9.92269i	0.642014	−	0.363052i
$748$	21.2839	+	7.74671i	0.778217	+	0.283248i
$749$	14.1910	−	19.0618i	0.518526	−	0.696502i
$750$	18.2477	+	14.5614i	0.666311	+	0.531708i
$751$	−37.5165	−	8.89157i	−1.36900	−	0.324458i	−0.520591	−	0.853806i	$-0.674289\pi$
$751$	−37.5165	−	8.89157i	−1.36900	−	0.324458i	−0.848405	+	0.529348i	$0.822437\pi$
$752$	−4.81660	+	11.1661i	−0.175643	+	0.407187i
$753$	−25.9436	−	33.1142i	−0.945436	−	1.20675i
$754$	−57.0709	+	37.5362i	−2.07840	+	1.36699i
$755$	−0.00634611	−	0.0109918i	−0.000230959	−	0.000400032i
$756$	21.0874	+	15.1911i	0.766941	+	0.552493i
$757$	25.4729	−	44.1204i	0.925829	−	1.60358i	0.135606	−	0.990763i	$-0.456702\pi$
$757$	25.4729	−	44.1204i	0.925829	−	1.60358i	0.790223	−	0.612820i	$-0.209965\pi$
$758$	1.27148	+	21.8305i	0.0461824	+	0.792921i
$759$	2.02655	+	6.20860i	0.0735590	+	0.225358i
$760$	−6.52527	+	0.762694i	−0.236696	+	0.0276658i
$761$	−26.7225	+	28.3242i	−0.968690	+	1.02675i	0.0309391	+	0.999521i	$0.490150\pi$
$761$	−26.7225	+	28.3242i	−0.968690	+	1.02675i	−0.999629	+	0.0272302i	$0.991331\pi$
$762$	32.2085	−	28.4062i	1.16679	−	1.02905i
$763$	3.22943	+	0.377466i	0.116913	+	0.0136652i
$764$	14.4293	−	12.1076i	0.522033	−	0.438038i
$765$	13.2641	−	0.653605i	0.479564	−	0.0236312i
$766$	−0.504379	−	0.423224i	−0.0182239	−	0.0152917i
$767$	7.64258	+	8.10067i	0.275958	+	0.292498i
$768$	−1.95193	−	0.179568i	−0.0704342	−	0.00647961i
$769$	30.5189

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94437 + 0.976500i) q^{2} +(-1.52821 + 0.815208i) q^{3} +(1.63271 + 2.19311i) q^{4} +(-0.185416 - 0.619334i) q^{5} +(-3.76746 + 0.0927672i) q^{6} +(-0.724564 - 1.67973i) q^{7} +(0.277373 + 1.57306i) q^{8} +(1.67087 - 2.49162i) q^{9} +(0.244261 - 1.38527i) q^{10} +(-1.17723 + 0.279008i) q^{11} +(-4.28297 - 2.02054i) q^{12} +(4.45604 + 2.93078i) q^{13} +(0.231433 - 3.97355i) q^{14} +(0.788242 + 0.795322i) q^{15} +(0.571538 - 1.90907i) q^{16} +(-6.43434 + 2.34191i) q^{17} +(5.68186 - 3.21304i) q^{18} +(-5.97823 - 2.17590i) q^{19} +(1.05554 - 1.41783i) q^{20} +(2.47662 + 1.97631i) q^{21} +(-2.56142 - 0.607068i) q^{22} +(-1.23445 + 2.86177i) q^{23} +(-1.70626 - 2.17786i) q^{24} +(3.82824 - 2.51788i) q^{25} +(5.80229 + 10.0499i) q^{26} +(-0.522256 + 5.16984i) q^{27} +(2.50083 - 4.33156i) q^{28} +(0.342261 + 5.87639i) q^{29} +(0.756004 + 2.31612i) q^{30} +(2.75457 - 0.321963i) q^{31} +(5.16779 - 5.47754i) q^{32} +(1.57161 - 1.38607i) q^{33} +(-14.7976 - 1.72959i) q^{34} +(-0.905967 + 0.760197i) q^{35} +(8.19245 - 0.403694i) q^{36} +(-1.09453 - 0.918418i) q^{37} +(-9.49913 - 10.0685i) q^{38} +(-9.19898 - 0.846262i) q^{39} +(0.922821 - 0.463458i) q^{40} +(0.996758 - 0.500591i) q^{41} +(2.88559 + 6.26110i) q^{42} +(6.61155 + 7.00783i) q^{43} +(-2.53397 - 2.12625i) q^{44} +(-1.85295 - 0.572840i) q^{45} +(-5.19473 + 4.35890i) q^{46} +(-6.06108 - 0.708439i) q^{47} +(0.682857 + 3.38339i) q^{48} +(2.50720 - 2.65747i) q^{49} +(9.90223 - 1.15740i) q^{50} +(7.92390 - 8.82426i) q^{51} +(0.847890 + 14.5577i) q^{52} +(4.26135 - 7.38088i) q^{53} +(-6.06381 + 9.54211i) q^{54} +(0.391077 + 0.677365i) q^{55} +(2.44134 - 1.60569i) q^{56} +(10.9098 - 1.54827i) q^{57} +(-5.07281 + 11.7601i) q^{58} +(2.03183 + 0.481552i) q^{59} +(-0.457257 + 3.02723i) q^{60} +(-2.14382 + 2.87965i) q^{61} +(5.67029 + 2.06382i) q^{62} +(-5.39591 - 1.00127i) q^{63} +(11.6517 - 4.24088i) q^{64} +(0.988911 - 3.30319i) q^{65} +(4.40929 - 1.16036i) q^{66} +(-0.0709235 + 1.21771i) q^{67} +(-15.6415 - 10.2876i) q^{68} +(-0.446439 - 5.37972i) q^{69} +(-2.50387 + 0.593428i) q^{70} +(1.41528 - 8.02646i) q^{71} +(4.38293 + 1.93727i) q^{72} +(1.11524 + 6.32482i) q^{73} +(-1.23133 - 2.85455i) q^{74} +(-3.79778 + 6.96867i) q^{75} +(-4.98873 - 16.6635i) q^{76} +(1.32164 + 1.77527i) q^{77} +(-17.0599 - 10.6283i) q^{78} +(-12.7417 - 6.39915i) q^{79} -1.28832 q^{80} +(-3.41638 - 8.32637i) q^{81} +2.42689 q^{82} +(6.00472 + 3.01569i) q^{83} +(-0.290674 + 8.65824i) q^{84} +(2.64346 + 3.55078i) q^{85} +(6.01216 + 20.0820i) q^{86} +(-5.31353 - 8.70136i) q^{87} +(-0.765429 - 1.77446i) q^{88} +(-2.70557 - 15.3441i) q^{89} +(-3.04345 - 2.92322i) q^{90} +(1.69423 - 9.60848i) q^{91} +(-8.29166 + 1.96516i) q^{92} +(-3.94710 + 2.73757i) q^{93} +(-11.0932 - 7.29611i) q^{94} +(-0.239145 + 4.10597i) q^{95} +(-3.43215 + 12.5837i) q^{96} +(1.06957 - 3.57262i) q^{97} +(7.46994 - 2.71884i) q^{98} +(-1.27181 + 3.39940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

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