LMFDB - Embedded newform 135.2.p.a.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (of order $18$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.4
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06000 + 1.26326i) q^{2} +(0.958575 + 1.44261i) q^{3} +(-0.124928 - 0.708504i) q^{4} +(-2.00944 + 0.980894i) q^{5} +(-2.83849 - 0.318243i) q^{6} +(1.22191 + 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +(-1.16227 + 2.76571i) q^{9} +O(q^{10})$	\(q+(-1.06000 + 1.26326i) q^{2} +(0.958575 + 1.44261i) q^{3} +(-0.124928 - 0.708504i) q^{4} +(-2.00944 + 0.980894i) q^{5} +(-2.83849 - 0.318243i) q^{6} +(1.22191 + 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +(-1.16227 + 2.76571i) q^{9} +(0.890884 - 3.57820i) q^{10} +(3.30366 - 1.20243i) q^{11} +(0.902344 - 0.859377i) q^{12} +(-0.380059 - 0.452936i) q^{13} +(-1.56741 + 1.31521i) q^{14} +(-3.34125 - 1.95858i) q^{15} +(4.62449 - 1.68318i) q^{16} +(-4.46967 + 2.58056i) q^{17} +(-2.26180 - 4.39990i) q^{18} +(-1.41748 + 2.45515i) q^{19} +(0.946003 + 1.30115i) q^{20} +(0.860474 + 1.96928i) q^{21} +(-1.98290 + 5.44797i) q^{22} +(6.59324 - 1.16257i) q^{23} +(-0.229849 - 3.65042i) q^{24} +(3.07569 - 3.94210i) q^{25} +0.975040 q^{26} +(-5.10397 + 0.974431i) q^{27} -0.892646i q^{28} +(7.21421 + 6.05345i) q^{29} +(6.01593 - 2.14477i) q^{30} +(0.196771 + 1.11595i) q^{31} +(-1.33116 + 3.65733i) q^{32} +(4.90146 + 3.61329i) q^{33} +(1.47793 - 8.38176i) q^{34} +(-2.66670 + 0.765621i) q^{35} +(2.10471 + 0.477957i) q^{36} +(4.06570 - 2.34734i) q^{37} +(-1.59896 - 4.39311i) q^{38} +(0.289098 - 0.982452i) q^{39} +(4.71061 + 0.327827i) q^{40} +(4.43129 - 3.71830i) q^{41} +(-3.39982 - 1.00044i) q^{42} +(0.739520 + 2.03181i) q^{43} +(-1.26465 - 2.19044i) q^{44} +(-0.377357 - 6.69758i) q^{45} +(-5.52022 + 9.56131i) q^{46} +(6.14268 + 1.08312i) q^{47} +(6.86110 + 5.05791i) q^{48} +(-5.13120 - 1.86760i) q^{49} +(1.71966 + 8.06403i) q^{50} +(-8.00727 - 3.97434i) q^{51} +(-0.273427 + 0.325858i) q^{52} -8.21098i q^{53} +(4.17926 - 7.48054i) q^{54} +(-5.45905 + 5.65676i) q^{55} +(-2.00717 - 1.68421i) q^{56} +(-4.90059 + 0.308566i) q^{57} +(-15.2942 + 2.69677i) q^{58} +(-12.6981 - 4.62173i) q^{59} +(-0.970247 + 2.61197i) q^{60} +(-1.38440 + 7.85133i) q^{61} +(-1.61831 - 0.934331i) q^{62} +(-2.01608 + 3.12903i) q^{63} +(1.71215 + 2.96553i) q^{64} +(1.20799 + 0.537351i) q^{65} +(-9.76008 + 2.36173i) q^{66} +(-2.83000 - 3.37266i) q^{67} +(2.38673 + 2.84439i) q^{68} +(7.99725 + 8.39709i) q^{69} +(1.85953 - 4.18030i) q^{70} +(-3.43788 - 5.95458i) q^{71} +(5.04582 - 3.83078i) q^{72} +(-1.23957 - 0.715668i) q^{73} +(-1.34436 + 7.62423i) q^{74} +(8.63520 + 0.658243i) q^{75} +(1.91656 + 0.697573i) q^{76} +(4.29586 - 0.757476i) q^{77} +(0.934649 + 1.40661i) q^{78} +(-0.970806 - 0.814603i) q^{79} +(-7.64162 + 7.91838i) q^{80} +(-6.29826 - 6.42899i) q^{81} +9.53928i q^{82} +(0.982501 - 1.17090i) q^{83} +(1.28774 - 0.855668i) q^{84} +(6.45027 - 9.56976i) q^{85} +(-3.35061 - 1.21952i) q^{86} +(-1.81742 + 16.2100i) q^{87} +(-7.31144 - 1.28920i) q^{88} +(6.52774 - 11.3064i) q^{89} +(8.86079 + 6.62275i) q^{90} +(-0.366811 - 0.635335i) q^{91} +(-1.64736 - 4.52610i) q^{92} +(-1.42126 + 1.35358i) q^{93} +(-7.87952 + 6.61170i) q^{94} +(0.440100 - 6.32387i) q^{95} +(-6.55214 + 1.58548i) q^{96} +(-4.74011 - 13.0234i) q^{97} +(7.79835 - 4.50238i) q^{98} +(-0.514163 + 10.5345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.06000	+	1.26326i	−0.749535	+	0.893261i	−0.997138	−	0.0756008i	$-0.975913\pi$
$2$	−1.06000	+	1.26326i	−0.749535	+	0.893261i	0.247604	+	0.968861i	$0.420357\pi$
$3$	0.958575	+	1.44261i	0.553433	+	0.832893i
$3$	0.958575	+	1.44261i	0.553433	+	0.832893i
$4$	−0.124928	−	0.708504i	−0.0624641	−	0.354252i
$5$	−2.00944	+	0.980894i	−0.898649	+	0.438669i
$5$	−2.00944	+	0.980894i	−0.898649	+	0.438669i
$6$	−2.83849	−	0.318243i	−1.15881	−	0.129922i
$7$	1.22191	+	0.215456i	0.461840	+	0.0814348i	0.399727	−	0.916634i	$-0.369105\pi$
$7$	1.22191	+	0.215456i	0.461840	+	0.0814348i	0.0621128	+	0.998069i	$0.480216\pi$
$8$	−1.82882	−	1.05587i	−0.646587	−	0.373307i
$9$	−1.16227	+	2.76571i	−0.387423	+	0.921902i
$10$	0.890884	−	3.57820i	0.281722	−	1.13153i
$11$	3.30366	−	1.20243i	0.996092	−	0.362548i	0.208016	−	0.978125i	$-0.433299\pi$
$11$	3.30366	−	1.20243i	0.996092	−	0.362548i	0.788076	+	0.615578i	$0.211077\pi$
$12$	0.902344	−	0.859377i	0.260484	−	0.248081i
$13$	−0.380059	−	0.452936i	−0.105409	−	0.125622i	0.710760	−	0.703434i	$-0.248351\pi$
$13$	−0.380059	−	0.452936i	−0.105409	−	0.125622i	−0.816170	+	0.577812i	$0.803907\pi$
$14$	−1.56741	+	1.31521i	−0.418907	+	0.351505i
$15$	−3.34125	−	1.95858i	−0.862707	−	0.505704i
$16$	4.62449	−	1.68318i	1.15612	−	0.420794i
$17$	−4.46967	+	2.58056i	−1.08405	+	0.625879i	−0.931987	−	0.362491i	$-0.881926\pi$
$17$	−4.46967	+	2.58056i	−1.08405	+	0.625879i	−0.152067	+	0.988370i	$0.548593\pi$
$18$	−2.26180	−	4.39990i	−0.533112	−	1.03707i
$19$	−1.41748	+	2.45515i	−0.325192	+	0.563250i	−0.981551	−	0.191199i	$-0.938762\pi$
$19$	−1.41748	+	2.45515i	−0.325192	+	0.563250i	0.656359	+	0.754449i	$0.272096\pi$
$20$	0.946003	+	1.30115i	0.211533	+	0.290947i
$21$	0.860474	+	1.96928i	0.187771	+	0.429732i
$22$	−1.98290	+	5.44797i	−0.422756	+	1.16151i
$23$	6.59324	−	1.16257i	1.37479	−	0.242412i	0.563043	−	0.826427i	$-0.309630\pi$
$23$	6.59324	−	1.16257i	1.37479	−	0.242412i	0.811742	+	0.584016i	$0.198519\pi$
$24$	−0.229849	−	3.65042i	−0.0469177	−	0.745139i
$25$	3.07569	−	3.94210i	0.615138	−	0.788419i
$26$	0.975040			0.191221
$27$	−5.10397	+	0.974431i	−0.982259	+	0.187529i
$28$		−	0.892646i		−	0.168694i
$29$	7.21421	+	6.05345i	1.33965	+	1.12410i	0.981717	+	0.190348i	$0.0609616\pi$
$29$	7.21421	+	6.05345i	1.33965	+	1.12410i	0.357929	+	0.933749i	$0.383483\pi$
$30$	6.01593	−	2.14477i	1.09835	−	0.391579i
$31$	0.196771	+	1.11595i	0.0353412	+	0.200430i	0.997366	−	0.0725319i	$-0.0231079\pi$
$31$	0.196771	+	1.11595i	0.0353412	+	0.200430i	−0.962025	+	0.272962i	$0.911997\pi$
$32$	−1.33116	+	3.65733i	−0.235318	+	0.646531i
$33$	4.90146	+	3.61329i	0.853234	+	0.628992i
$34$	1.47793	−	8.38176i	0.253463	−	1.43746i
$35$	−2.66670	+	0.765621i	−0.450754	+	0.129414i
$36$	2.10471	+	0.477957i	0.350785	+	0.0796595i
$37$	4.06570	−	2.34734i	0.668398	−	0.385900i	−0.127072	−	0.991894i	$-0.540558\pi$
$37$	4.06570	−	2.34734i	0.668398	−	0.385900i	0.795469	+	0.605994i	$0.207224\pi$
$38$	−1.59896	−	4.39311i	−0.259386	−	0.712657i
$39$	0.289098	−	0.982452i	0.0462927	−	0.157318i
$40$	4.71061	+	0.327827i	0.744813	+	0.0518341i
$41$	4.43129	−	3.71830i	0.692052	−	0.580700i	−0.227448	−	0.973790i	$-0.573038\pi$
$41$	4.43129	−	3.71830i	0.692052	−	0.580700i	0.919500	+	0.393090i	$0.128594\pi$
$42$	−3.39982	−	1.00044i	−0.524603	−	0.154371i
$43$	0.739520	+	2.03181i	0.112776	+	0.309849i	0.983222	−	0.182415i	$-0.0583916\pi$
$43$	0.739520	+	2.03181i	0.112776	+	0.309849i	−0.870446	+	0.492264i	$0.836169\pi$
$44$	−1.26465	−	2.19044i	−0.190653	−	0.330221i
$45$	−0.377357	−	6.69758i	−0.0562530	−	0.998417i
$46$	−5.52022	+	9.56131i	−0.813913	+	1.40974i
$47$	6.14268	+	1.08312i	0.896002	+	0.157989i	0.602641	−	0.798012i	$-0.294115\pi$
$47$	6.14268	+	1.08312i	0.896002	+	0.157989i	0.293361	+	0.956002i	$0.405226\pi$
$48$	6.86110	+	5.05791i	0.990314	+	0.730046i
$49$	−5.13120	−	1.86760i	−0.733029	−	0.266801i
$50$	1.71966	+	8.06403i	0.243196	+	1.14043i
$51$	−8.00727	−	3.97434i	−1.12124	−	0.556519i
$52$	−0.273427	+	0.325858i	−0.0379175	+	0.0451883i
$53$		−	8.21098i		−	1.12787i	−0.825821	−	0.563933i	$-0.809288\pi$
$53$		−	8.21098i		−	1.12787i	0.825821	−	0.563933i	$-0.190712\pi$
$54$	4.17926	−	7.48054i	0.568725	−	1.01797i
$55$	−5.45905	+	5.65676i	−0.736098	+	0.762758i
$56$	−2.00717	−	1.68421i	−0.268219	−	0.225063i
$57$	−4.90059	+	0.308566i	−0.649099	+	0.0408706i
$58$	−15.2942	+	2.69677i	−2.00822	+	0.354104i
$59$	−12.6981	−	4.62173i	−1.65315	−	0.601698i	−0.663886	−	0.747833i	$-0.731094\pi$
$59$	−12.6981	−	4.62173i	−1.65315	−	0.601698i	−0.989265	+	0.146136i	$0.953316\pi$
$60$	−0.970247	+	2.61197i	−0.125258	+	0.337204i
$61$	−1.38440	+	7.85133i	−0.177254	+	1.00526i	0.758255	+	0.651958i	$0.226052\pi$
$61$	−1.38440	+	7.85133i	−0.177254	+	1.00526i	−0.935509	+	0.353302i	$0.885059\pi$
$62$	−1.61831	−	0.934331i	−0.205525	−	0.118660i
$63$	−2.01608	+	3.12903i	−0.254002	+	0.394221i
$64$	1.71215	+	2.96553i	0.214019	+	0.370691i
$65$	1.20799	+	0.537351i	0.149832	+	0.0666502i
$66$	−9.76008	+	2.36173i	−1.20138	+	0.290709i
$67$	−2.83000	−	3.37266i	−0.345739	−	0.412036i	0.564952	−	0.825124i	$-0.308895\pi$
$67$	−2.83000	−	3.37266i	−0.345739	−	0.412036i	−0.910691	+	0.413088i	$0.864450\pi$
$68$	2.38673	+	2.84439i	0.289433	+	0.344933i
$69$	7.99725	+	8.39709i	0.962755	+	1.01089i
$70$	1.85953	−	4.18030i	0.222256	−	0.499641i
$71$	−3.43788	−	5.95458i	−0.408001	−	0.706679i	0.586664	−	0.809830i	$-0.300441\pi$
$71$	−3.43788	−	5.95458i	−0.408001	−	0.706679i	−0.994666	+	0.103151i	$0.967107\pi$
$72$	5.04582	−	3.83078i	0.594655	−	0.451462i
$73$	−1.23957	−	0.715668i	−0.145081	−	0.0837626i	0.425702	−	0.904863i	$-0.360027\pi$
$73$	−1.23957	−	0.715668i	−0.145081	−	0.0837626i	−0.570783	+	0.821101i	$0.693360\pi$
$74$	−1.34436	+	7.62423i	−0.156278	+	0.886298i
$75$	8.63520	+	0.658243i	0.997107	+	0.0760073i
$76$	1.91656	+	0.697573i	0.219845	+	0.0800171i
$77$	4.29586	−	0.757476i	0.489559	−	0.0863224i
$78$	0.934649	+	1.40661i	0.105828	+	0.159267i
$79$	−0.970806	−	0.814603i	−0.109224	−	0.0916500i	0.586540	−	0.809920i	$-0.300490\pi$
$79$	−0.970806	−	0.814603i	−0.109224	−	0.0916500i	−0.695764	+	0.718270i	$0.744934\pi$
$80$	−7.64162	+	7.91838i	−0.854359	+	0.885302i
$81$	−6.29826	−	6.42899i	−0.699807	−	0.714332i
$82$			9.53928i			1.05344i
$83$	0.982501	−	1.17090i	0.107844	−	0.128523i	−0.709423	−	0.704783i	$-0.751044\pi$
$83$	0.982501	−	1.17090i	0.107844	−	0.128523i	0.817266	+	0.576260i	$0.195489\pi$
$84$	1.28774	−	0.855668i	0.140504	−	0.0933610i
$85$	6.45027	−	9.56976i	0.699630	−	1.03799i
$86$	−3.35061	−	1.21952i	−0.361305	−	0.131504i
$87$	−1.81742	+	16.2100i	−0.194848	+	1.73789i
$88$	−7.31144	−	1.28920i	−0.779402	−	0.137430i
$89$	6.52774	−	11.3064i	0.691939	−	1.19847i	−0.279262	−	0.960215i	$-0.590090\pi$
$89$	6.52774	−	11.3064i	0.691939	−	1.19847i	0.971202	−	0.238259i	$-0.0765767\pi$
$90$	8.86079	+	6.62275i	0.934010	+	0.698099i
$91$	−0.366811	−	0.635335i	−0.0384522	−	0.0666012i
$92$	−1.64736	−	4.52610i	−0.171750	−	0.471878i
$93$	−1.42126	+	1.35358i	−0.147378	+	0.140360i
$94$	−7.87952	+	6.61170i	−0.812711	+	0.681945i
$95$	0.440100	−	6.32387i	0.0451533	−	0.648815i
$96$	−6.55214	+	1.58548i	−0.668724	+	0.161817i
$97$	−4.74011	−	13.0234i	−0.481286	−	1.32232i	−0.908392	−	0.418120i	$-0.862689\pi$
$97$	−4.74011	−	13.0234i	−0.481286	−	1.32232i	0.427106	−	0.904202i	$-0.359533\pi$
$98$	7.79835	−	4.50238i	0.787753	−	0.454809i
$99$	−0.514163	+	10.5345i	−0.0516753	+	1.05876i
$100$	−3.17723	−	1.68666i	−0.317723	−	0.168666i
$101$	2.04974	−	11.6247i	0.203957	−	1.15670i	−0.695115	−	0.718898i	$-0.744647\pi$
$101$	2.04974	−	11.6247i	0.203957	−	1.15670i	0.899072	−	0.437800i	$-0.144242\pi$
$102$	13.5084	−	5.90246i	1.33753	−	0.584431i
$103$	0.837596	−	2.30128i	0.0825308	−	0.226751i	−0.891563	−	0.452897i	$-0.850390\pi$
$103$	0.837596	−	2.30128i	0.0825308	−	0.226751i	0.974093	+	0.226146i	$0.0726126\pi$
$104$	0.216818	+	1.22963i	0.0212607	+	0.120576i
$105$	−3.66073	−	3.11311i	−0.357250	−	0.303809i
$106$	10.3726	+	8.70366i	1.00748	+	0.845374i
$107$			6.83945i			0.661195i	0.943772	+	0.330597i	$0.107250\pi$
$107$			6.83945i			0.661195i	−0.943772	+	0.330597i	$0.892750\pi$
$108$	1.32802	+	3.49445i	0.127789	+	0.336253i
$109$	18.7944			1.80018			0.900088	−	0.435708i	$-0.143502\pi$
$109$	18.7944			1.80018			0.900088	+	0.435708i	$0.143502\pi$
$110$	−1.35937	−	12.8924i	−0.129611	−	1.22924i
$111$	7.28358	+	3.61514i	0.691327	+	0.343134i
$112$	6.01338	−	1.06032i	0.568211	−	0.100191i
$113$	−4.71959	+	12.9670i	−0.443982	+	1.21983i	0.492870	+	0.870103i	$0.335948\pi$
$113$	−4.71959	+	12.9670i	−0.443982	+	1.21983i	−0.936852	+	0.349727i	$0.886274\pi$
$114$	4.80484	−	6.51781i	0.450014	−	0.610449i
$115$	−12.1084	+	8.80338i	−1.12911	+	0.820919i
$116$	3.38763	−	5.86754i	0.314533	−	0.544788i
$117$	1.69442	−	0.524697i	0.156649	−	0.0485083i
$118$	19.2985	−	11.1420i	1.77657	−	1.02570i
$119$	−6.01754	+	2.19021i	−0.551627	+	0.200776i
$120$	4.04254	+	7.10984i	0.369032	+	0.649037i
$121$	1.04185	−	0.874216i	0.0947136	−	0.0794742i
$122$	−8.45081	−	10.0713i	−0.765101	−	0.911811i
$123$	9.61179	+	2.82838i	0.866666	+	0.255026i
$124$	0.766069	−	0.278826i	0.0687950	−	0.0250393i
$125$	−2.31364	+	10.9383i	−0.206938	+	0.978354i
$126$	−1.81574	−	5.86362i	−0.161759	−	0.522372i
$127$	−7.40277	−	4.27399i	−0.656890	−	0.379255i	0.134201	−	0.990954i	$-0.457153\pi$
$127$	−7.40277	−	4.27399i	−0.656890	−	0.379255i	−0.791091	+	0.611699i	$0.790486\pi$
$128$	−13.2270	−	2.33227i	−1.16911	−	0.206146i
$129$	−2.22224	+	3.01449i	−0.195657	+	0.265411i
$130$	−1.95928	+	0.956412i	−0.171841	+	0.0838828i
$131$	1.68189	+	9.53845i	0.146947	+	0.833379i	0.965783	+	0.259351i	$0.0835087\pi$
$131$	1.68189	+	9.53845i	0.146947	+	0.833379i	−0.818836	+	0.574028i	$0.805380\pi$
$132$	1.94770	−	3.92410i	0.169525	−	0.341549i
$133$	−2.26101	+	2.69457i	−0.196055	+	0.233649i
$134$	7.26035			0.627198
$135$	9.30030	−	6.96451i	0.800442	−	0.599410i
$136$	10.8990			0.934580
$137$	9.51323	−	11.3374i	0.812770	−	0.968622i	−0.187136	−	0.982334i	$-0.559920\pi$
$137$	9.51323	−	11.3374i	0.812770	−	0.968622i	0.999906	+	0.0137123i	$0.00436489\pi$
$138$	−19.0848	+	1.20168i	−1.62461	+	0.102294i
$139$	−0.474713	−	2.69223i	−0.0402646	−	0.228352i	0.958034	−	0.286653i	$-0.0925428\pi$
$139$	−0.474713	−	2.69223i	−0.0402646	−	0.228352i	−0.998299	+	0.0583011i	$0.981432\pi$
$140$	0.875591	+	1.79372i	0.0740010	+	0.151597i
$141$	4.32570	+	9.89977i	0.364289	+	0.833711i
$142$	11.1664	+	1.96893i	0.937060	+	0.165229i
$143$	−1.80021	−	1.03935i	−0.150541	−	0.0869151i
$144$	−0.719730	+	14.7463i	−0.0599775	+	1.22886i
$145$	−20.4343	−	5.08765i	−1.69698	−	0.422506i
$146$	2.21803	−	0.807296i	0.183565	−	0.0668123i
$147$	−2.22441	−	9.19258i	−0.183466	−	0.758191i
$148$	−2.17102	−	2.58732i	−0.178456	−	0.212676i
$149$	−14.9253	+	12.5238i	−1.22273	+	1.02599i	−0.224054	+	0.974577i	$0.571929\pi$
$149$	−14.9253	+	12.5238i	−1.22273	+	1.02599i	−0.998677	+	0.0514162i	$0.983626\pi$
$150$	−9.98486	+	10.2108i	−0.815261	+	0.833707i
$151$	−12.9070	+	4.69775i	−1.05035	+	0.382297i	−0.808796	−	0.588089i	$-0.799880\pi$
$151$	−12.9070	+	4.69775i	−1.05035	+	0.382297i	−0.241557	+	0.970387i	$0.577658\pi$
$152$	5.18465	−	2.99336i	0.420530	−	0.242793i
$153$	−1.94213	−	15.3611i	−0.157012	−	1.24187i
$154$	−3.59673	+	6.22972i	−0.289833	+	0.502005i
$155$	−1.49002	−	2.04941i	−0.119682	−	0.164613i
$156$	−0.732187	−	0.0820907i	−0.0586219	−	0.00657252i
$157$	4.04287	−	11.1077i	0.322656	−	0.886491i	−0.667258	−	0.744826i	$-0.732532\pi$
$157$	4.04287	−	11.1077i	0.322656	−	0.886491i	0.989915	−	0.141665i	$-0.0452455\pi$
$158$	2.05811	−	0.362901i	0.163735	−	0.0288708i
$159$	11.8453	−	7.87084i	0.939392	−	0.624198i
$160$	−0.912572	−	8.65492i	−0.0721451	−	0.684231i
$161$	8.30684			0.654671
$162$	14.7977	−	1.14161i	1.16261	−	0.0896932i
$163$			13.4522i			1.05366i	0.849972	+	0.526828i	$0.176619\pi$
$163$			13.4522i			1.05366i	−0.849972	+	0.526828i	$0.823381\pi$
$164$	−3.18802	−	2.67507i	−0.248943	−	0.208888i
$165$	−13.3934	−	2.45287i	−1.04268	−	0.190955i
$166$	0.437699	+	2.48231i	0.0339720	+	0.192665i
$167$	0.885201	−	2.43207i	0.0684989	−	0.188199i	−0.900720	−	0.434401i	$-0.856960\pi$
$167$	0.885201	−	2.43207i	0.0684989	−	0.188199i	0.969219	+	0.246201i	$0.0791824\pi$
$168$	0.505650	−	4.51002i	0.0390117	−	0.347955i
$169$	2.19672	−	12.4582i	0.168978	−	0.958324i
$170$	5.25181	+	18.2923i	0.402796	+	1.40296i
$171$	−5.14273	−	6.77388i	−0.393274	−	0.518011i
$172$	1.34716	−	0.777784i	0.102720	−	0.0593055i
$173$	5.65820	+	15.5458i	0.430185	+	1.18192i	0.945699	+	0.325042i	$0.105379\pi$
$173$	5.65820	+	15.5458i	0.430185	+	1.18192i	−0.515515	+	0.856881i	$0.672399\pi$
$174$	−18.5510	−	19.4785i	−1.40635	−	1.47666i
$175$	4.60758	−	4.15422i	0.348300	−	0.314029i
$176$	13.2539	−	11.1213i	0.999047	−	0.838300i
$177$	−5.50470	−	22.7487i	−0.413759	−	1.70990i
$178$	7.36349	+	20.2310i	0.551917	+	1.51638i
$179$	−0.606831	−	1.05106i	−0.0453567	−	0.0785601i	0.842456	−	0.538765i	$-0.181109\pi$
$179$	−0.606831	−	1.05106i	−0.0453567	−	0.0785601i	−0.887812	+	0.460205i	$0.847776\pi$
$180$	−4.69812	+	1.10408i	−0.350177	+	0.0822930i
$181$	1.84215	−	3.19070i	0.136926	−	0.237163i	−0.789405	−	0.613872i	$-0.789611\pi$
$181$	1.84215	−	3.19070i	0.136926	−	0.237163i	0.926332	+	0.376709i	$0.122944\pi$
$182$	1.19141	+	0.210078i	0.0883135	+	0.0155720i
$183$	−12.6535	+	5.52893i	−0.935373	+	0.408710i
$184$	−13.2854	−	4.83549i	−0.979413	−	0.356477i
$185$	−5.86730	+	8.70485i	−0.431372	+	0.639994i
$186$	−0.203391	−	3.23022i	−0.0149134	−	0.236851i
$187$	−11.6633	+	13.8998i	−0.852906	+	1.01645i
$188$		−	4.48743i		−	0.327279i
$189$	−6.44655	+	0.0909880i	−0.468917	+	0.00661840i
$190$	7.52219	+	7.25928i	0.545717	+	0.526643i
$191$	2.91058	+	2.44226i	0.210602	+	0.176716i	0.741987	−	0.670415i	$-0.233884\pi$
$191$	2.91058	+	2.44226i	0.210602	+	0.176716i	−0.531385	+	0.847131i	$0.678328\pi$
$192$	−2.63689	+	5.31265i	−0.190301	+	0.383407i
$193$	8.95492	−	1.57899i	0.644589	−	0.113658i	0.158209	−	0.987406i	$-0.449428\pi$
$193$	8.95492	−	1.57899i	0.644589	−	0.113658i	0.486380	+	0.873747i	$0.338317\pi$
$194$	21.4764	+	7.81678i	1.54192	+	0.561212i
$195$	0.382757	+	2.25775i	0.0274098	+	0.161681i
$196$	−0.682172	+	3.86879i	−0.0487266	+	0.276342i
$197$	5.83859	+	3.37091i	0.415982	+	0.240167i	0.693357	−	0.720594i	$-0.256131\pi$
$197$	5.83859	+	3.37091i	0.415982	+	0.240167i	−0.277375	+	0.960762i	$0.589464\pi$
$198$	−12.7628	−	11.8161i	−0.907015	−	0.839736i
$199$	−5.30284	−	9.18479i	−0.375909	−	0.651093i	0.614554	−	0.788875i	$-0.289336\pi$
$199$	−5.30284	−	9.18479i	−0.375909	−	0.651093i	−0.990463	+	0.137782i	$0.956003\pi$
$200$	−9.78725	+	3.96186i	−0.692063	+	0.280146i
$201$	2.15268	−	7.31553i	0.151838	−	0.515998i
$202$	12.5123	+	14.9115i	0.880360	+	1.04917i
$203$	7.51089	+	8.95113i	0.527161	+	0.628246i
$204$	−1.81550	+	6.16969i	−0.127110	+	0.431965i
$205$	−5.25716	+	11.8183i	−0.367176	+	0.825427i
$206$	2.01926	+	3.49746i	0.140688	+	0.243680i
$207$	−4.44780	+	19.5862i	−0.309144	+	1.36133i
$208$	−2.51995	−	1.45489i	−0.174727	−	0.100879i
$209$	−1.73072	+	9.81541i	−0.119717	+	0.678946i
$210$	7.81305	−	1.32455i	0.539152	−	0.0914025i
$211$	16.7832	+	6.10860i	1.15541	+	0.420534i	0.847454	−	0.530868i	$-0.178134\pi$
$211$	16.7832	+	6.10860i	1.15541	+	0.420534i	0.307952	+	0.951402i	$0.400356\pi$
$212$	−5.81751	+	1.02578i	−0.399548	+	0.0704511i
$213$	5.29470	−	10.6674i	0.362787	−	0.730921i
$214$	−8.64002	−	7.24983i	−0.590619	−	0.495588i
$215$	−3.47902	−	3.35742i	−0.237267	−	0.228974i
$216$	10.3631	+	3.60708i	0.705122	+	0.245430i
$217$			1.40598i			0.0954443i
$218$	−19.9221	+	23.7422i	−1.34929	+	1.60803i
$219$	−0.155791	−	2.47425i	−0.0105274	−	0.167194i
$220$	4.68983	+	3.16107i	0.316188	+	0.213119i
$221$	2.86757	+	1.04371i	0.192894	+	0.0702075i
$222$	−12.2875	+	5.36900i	−0.824682	+	0.360344i
$223$	19.2137	+	3.38789i	1.28664	+	0.226870i	0.774798	−	0.632209i	$-0.217851\pi$
$223$	19.2137	+	3.38789i	1.28664	+	0.226870i	0.511844	+	0.859078i	$0.328963\pi$
$224$	−2.41456	+	4.18213i	−0.161329	+	0.279431i
$225$	7.32790	+	13.0882i	0.488526	+	0.872549i
$226$	−11.3779	−	19.7071i	−0.756846	−	1.31090i
$227$	1.25836	+	3.45732i	0.0835203	+	0.229470i	0.974422	−	0.224726i	$-0.0721487\pi$
$227$	1.25836	+	3.45732i	0.0835203	+	0.229470i	−0.890902	+	0.454196i	$0.849927\pi$
$228$	0.830843	+	3.43354i	0.0550239	+	0.227392i
$229$	−3.32291	+	2.78825i	−0.219584	+	0.184253i	−0.745943	−	0.666009i	$-0.768001\pi$
$229$	−3.32291	+	2.78825i	−0.219584	+	0.184253i	0.526360	+	0.850262i	$0.323557\pi$
$230$	1.71392	−	24.6276i	0.113013	−	1.62390i
$231$	5.21065	+	5.47117i	0.342835	+	0.359976i
$232$	−6.80187	−	18.6880i	−0.446564	−	1.22693i
$233$	−6.83118	+	3.94398i	−0.447525	+	0.258379i	−0.706784	−	0.707429i	$-0.749855\pi$
$233$	−6.83118	+	3.94398i	−0.447525	+	0.258379i	0.259259	+	0.965808i	$0.416522\pi$
$234$	−1.13326	+	2.69667i	−0.0740835	+	0.176287i
$235$	−13.4058	+	3.84886i	−0.874496	+	0.251072i
$236$	−1.68816	+	9.57403i	−0.109890	+	0.623216i
$237$	0.244567	−	2.18136i	0.0158864	−	0.141694i
$238$	3.61180	−	9.92335i	0.234119	−	0.643235i
$239$	−4.95815	−	28.1191i	−0.320716	−	1.81887i	−0.538210	−	0.842811i	$-0.680899\pi$
$239$	−4.95815	−	28.1191i	−0.320716	−	1.81887i	0.217493	−	0.976062i	$-0.430212\pi$
$240$	−18.7482	−	3.43354i	−1.21019	−	0.221634i
$241$	−10.0815	−	8.45937i	−0.649405	−	0.544916i	0.257485	−	0.966282i	$-0.417106\pi$
$241$	−10.0815	−	8.45937i	−0.649405	−	0.544916i	−0.906890	+	0.421367i	$0.861551\pi$
$242$			2.24280i			0.144173i
$243$	3.23719	−	15.2486i	0.207666	−	0.978200i
$244$	5.73565			0.367187
$245$	12.1428	−	1.28033i	0.775772	−	0.0817972i
$246$	−13.7615	+	9.14411i	−0.877401	+	0.583007i
$247$	1.65075	−	0.291072i	0.105035	−	0.0185205i
$248$	0.818435	−	2.24863i	0.0519707	−	0.142788i
$249$	2.63096	+	0.294975i	0.166730	+	0.0186933i
$250$	−11.3655	−	14.5174i	−0.718818	−	0.918160i
$251$	−13.5512	+	23.4713i	−0.855341	+	1.48149i	0.0209869	+	0.999780i	$0.493319\pi$
$251$	−13.5512	+	23.4713i	−0.855341	+	1.48149i	−0.876328	+	0.481715i	$0.840014\pi$
$252$	2.46880	+	1.03749i	0.155520	+	0.0653560i
$253$	20.3839	−	11.7687i	1.28153	−	0.739890i
$254$	13.2461	−	4.82119i	0.831135	−	0.302509i
$255$	19.9885	+	0.131912i	1.25173	+	0.00826067i
$256$	11.7205	−	9.83471i	0.732534	−	0.614669i
$257$	1.21645	+	1.44970i	0.0758798	+	0.0904300i	0.802649	−	0.596452i	$-0.203423\pi$
$257$	1.21645	+	1.44970i	0.0758798	+	0.0904300i	−0.726769	+	0.686882i	$0.758979\pi$
$258$	−1.45251	−	6.00263i	−0.0904292	−	0.373708i
$259$	5.47368	−	1.99226i	0.340118	−	0.123793i
$260$	0.229803	−	0.922994i	0.0142518	−	0.0572417i
$261$	−25.1269	+	12.9167i	−1.55532	+	0.799522i
$262$	−13.8324	−	7.98612i	−0.854566	−	0.493384i
$263$	−20.7228	−	3.65398i	−1.27782	−	0.225314i	−0.506766	−	0.862084i	$-0.669159\pi$
$263$	−20.7228	−	3.65398i	−1.27782	−	0.225314i	−0.771054	+	0.636770i	$0.780270\pi$
$264$	−5.14874	−	11.7834i	−0.316883	−	0.725217i
$265$	8.05411	+	16.4995i	0.494760	+	1.01355i
$266$	−1.00727	−	5.71250i	−0.0617596	−	0.350256i
$267$	22.5681	−	1.42100i	1.38114	−	0.0869638i
$268$	−2.03599	+	2.42640i	−0.124368	+	0.148216i
$269$	1.06528			0.0649512			0.0324756	−	0.999473i	$-0.489661\pi$
$269$	1.06528			0.0649512			0.0324756	+	0.999473i	$0.489661\pi$
$270$	−1.06034	+	19.1311i	−0.0645300	+	1.16428i
$271$	−5.32687			−0.323585			−0.161792	−	0.986825i	$-0.551727\pi$
$271$	−5.32687			−0.323585			−0.161792	+	0.986825i	$0.551727\pi$
$272$	−16.3264	+	19.4571i	−0.989934	+	1.17976i
$273$	0.564927	−	1.13818i	0.0341909	−	0.0688859i
$274$	4.23809	+	24.0354i	0.256032	+	1.45203i
$275$	5.42094	−	16.7217i	0.326895	−	1.00835i
$276$	4.95029	−	6.71511i	0.297972	−	0.404202i
$277$	16.9171	+	2.98294i	1.01645	+	0.179228i	0.656963	−	0.753923i	$-0.271841\pi$
$277$	16.9171	+	2.98294i	1.01645	+	0.179228i	0.359487	+	0.933150i	$0.382952\pi$
$278$	3.90419	+	2.25408i	0.234158	+	0.135191i
$279$	−3.31508	−	0.752817i	−0.198468	−	0.0450700i
$280$	5.68532	+	1.41551i	0.339763	+	0.0845927i
$281$	−11.6900	+	4.25480i	−0.697365	+	0.253820i	−0.666286	−	0.745697i	$-0.732117\pi$
$281$	−11.6900	+	4.25480i	−0.697365	+	0.253820i	−0.0310798	+	0.999517i	$0.509895\pi$
$282$	−17.0912	−	5.02929i	−1.01777	−	0.299490i
$283$	−13.3156	−	15.8689i	−0.791528	−	0.943306i	0.207865	−	0.978158i	$-0.433349\pi$
$283$	−13.3156	−	15.8689i	−0.791528	−	0.943306i	−0.999393	+	0.0348514i	$0.988904\pi$
$284$	−3.78936	+	3.17965i	−0.224857	+	0.188677i
$285$	9.54477	−	5.42701i	0.565383	−	0.321468i
$286$	3.22120	−	1.17242i	0.190474	−	0.0693268i
$287$	6.21578	−	3.58868i	0.366906	−	0.211833i
$288$	−8.56794	−	7.93240i	−0.504871	−	0.467421i
$289$	4.81863	−	8.34611i	0.283449	−	0.490948i
$290$	28.0874	−	20.4210i	1.64935	−	1.19916i
$291$	14.2439	−	19.3220i	0.834993	−	1.13268i
$292$	−0.352196	+	0.967650i	−0.0206107	+	0.0566274i
$293$	6.16081	−	1.08632i	0.359919	−	0.0634634i	0.00923499	−	0.999957i	$-0.497060\pi$
$293$	6.16081	−	1.08632i	0.359919	−	0.0634634i	0.350684	+	0.936494i	$0.385949\pi$
$294$	13.9705	+	6.93414i	0.814776	+	0.404407i
$295$	30.0495	−	3.16841i	1.74955	−	0.184472i
$296$	−9.91394			−0.576236
$297$	−15.6901	+	9.35638i	−0.910432	+	0.542912i
$298$		−	32.1299i		−	1.86123i
$299$	−3.03239	−	2.54448i	−0.175367	−	0.147151i
$300$	−0.612414	−	6.20030i	−0.0353577	−	0.357975i
$301$	0.465862	+	2.64203i	0.0268518	+	0.152284i
$302$	7.74692	−	21.2845i	0.445785	−	1.22478i
$303$	18.7348	−	8.18613i	1.07628	−	0.470281i
$304$	−2.42268	+	13.7397i	−0.138950	+	0.788025i
$305$	−4.91946	−	17.1347i	−0.281687	−	0.981131i
$306$	21.4637	+	13.8294i	1.22700	+	0.790573i
$307$	−15.8040	+	9.12444i	−0.901981	+	0.520759i	−0.877843	−	0.478949i	$-0.841018\pi$
$307$	−15.8040	+	9.12444i	−0.901981	+	0.520759i	−0.0241389	+	0.999709i	$0.507684\pi$
$308$	−1.07335	−	2.94900i	−0.0611597	−	0.168035i
$309$	4.12275	−	0.997617i	0.234535	−	0.0567525i
$310$	4.16837	+	0.290091i	0.236748	+	0.0164761i
$311$	−3.62362	+	3.04058i	−0.205477	+	0.172416i	−0.739719	−	0.672916i	$-0.765042\pi$
$311$	−3.62362	+	3.04058i	−0.205477	+	0.172416i	0.534242	+	0.845332i	$0.320597\pi$
$312$	−1.56605	+	1.49148i	−0.0886602	+	0.0844385i
$313$	11.8489	+	32.5545i	0.669737	+	1.84009i	0.526026	+	0.850469i	$0.323681\pi$
$313$	11.8489	+	32.5545i	0.669737	+	1.84009i	0.143711	+	0.989620i	$0.454096\pi$
$314$	9.74647	+	16.8814i	0.550025	+	0.952672i
$315$	0.981938	−	8.26516i	0.0553259	−	0.465689i
$316$	−0.455868	+	0.789587i	−0.0256446	+	0.0444177i
$317$	−1.01556	−	0.179070i	−0.0570395	−	0.0100576i	0.145056	−	0.989424i	$-0.453664\pi$
$317$	−1.01556	−	0.179070i	−0.0570395	−	0.0100576i	−0.202095	+	0.979366i	$0.564775\pi$
$318$	−2.61309	+	23.3068i	−0.146535	+	1.30698i
$319$	31.1122	+	11.3239i	1.74195	+	0.634018i
$320$	−6.34933	−	4.27961i	−0.354938	−	0.239238i
$321$	−9.86669	+	6.55613i	−0.550705	+	0.365927i
$322$	−8.80527	+	10.4937i	−0.490699	+	0.584792i
$323$		−	14.6316i		−	0.814124i
$324$	−3.76813	+	5.26550i	−0.209341	+	0.292528i
$325$	−2.95446	+	0.105135i	−0.163884	+	0.00583185i
$326$	−16.9936	−	14.2593i	−0.941189	−	0.789752i
$327$	18.0158	+	27.1130i	0.996278	+	1.49936i
$328$	−12.0301	+	2.12123i	−0.664251	+	0.117125i
$329$	7.27246	+	2.64696i	0.400943	+	0.145931i
$330$	17.2957	−	14.3194i	0.952096	−	0.788255i
$331$	2.20443	−	12.5020i	0.121167	−	0.687170i	−0.862344	−	0.506322i	$-0.831005\pi$
$331$	2.20443	−	12.5020i	0.121167	−	0.687170i	0.983511	−	0.180848i	$-0.0578842\pi$
$332$	−0.952329	−	0.549827i	−0.0522658	−	0.0301757i
$333$	1.76660	+	13.9728i	0.0968090	+	0.765703i
$334$	2.13403	+	3.69624i	0.116769	+	0.202249i
$335$	8.99492	+	4.00122i	0.491445	+	0.218610i
$336$	7.29390	+	7.65858i	0.397915	+	0.417810i
$337$	−5.97195	−	7.11709i	−0.325313	−	0.387693i	0.578456	−	0.815714i	$-0.303655\pi$
$337$	−5.97195	−	7.11709i	−0.325313	−	0.387693i	−0.903769	+	0.428021i	$0.859211\pi$
$338$	13.4095	+	15.9808i	0.729378	+	0.869239i
$339$	−23.2304	+	5.62126i	−1.26170	+	0.305305i
$340$	−7.58603	−	3.37450i	−0.411410	−	0.183008i
$341$	1.99192	+	3.45010i	0.107868	+	0.186833i
$342$	14.0085	+	0.683719i	0.757492	+	0.0369713i
$343$	−13.3892	−	7.73027i	−0.722950	−	0.417395i
$344$	0.792885	−	4.49667i	0.0427495	−	0.242444i
$345$	−24.3066	−	9.02899i	−1.30863	−	0.486105i
$346$	−25.6361	−	9.33077i	−1.37820	−	0.501625i
$347$	−24.7495	+	4.36400i	−1.32862	+	0.234272i	−0.792502	−	0.609870i	$-0.791222\pi$
$347$	−24.7495	+	4.36400i	−1.32862	+	0.234272i	−0.536120	+	0.844142i	$0.680111\pi$
$348$	11.7119	−	0.737440i	0.627823	−	0.0395310i
$349$	−1.83471	−	1.53950i	−0.0982096	−	0.0824076i	0.592361	−	0.805673i	$-0.298196\pi$
$349$	−1.83471	−	1.53950i	−0.0982096	−	0.0824076i	−0.690570	+	0.723265i	$0.742640\pi$
$350$	0.363825	+	10.2241i	0.0194473	+	0.546499i
$351$	2.38116	+	1.94143i	0.127097	+	0.103626i
$352$			13.6832i			0.729319i
$353$	−8.23024	+	9.80842i	−0.438051	+	0.522049i	−0.939227	−	0.343296i	$-0.888457\pi$
$353$	−8.23024	+	9.80842i	−0.438051	+	0.522049i	0.501176	+	0.865346i	$0.332901\pi$
$354$	34.5726	+	17.1598i	1.83751	+	0.912034i
$355$	12.7490	+	8.59318i	0.676648	+	0.456078i
$356$	−8.82611	−	3.21244i	−0.467783	−	0.170259i
$357$	−8.92789	−	6.58151i	−0.472514	−	0.348331i
$358$	1.97101	+	0.347542i	0.104171	+	0.0183682i
$359$	0.774475	−	1.34143i	0.0408753	−	0.0707980i	−0.844864	−	0.534981i	$-0.820319\pi$
$359$	0.774475	−	1.34143i	0.0408753	−	0.0707980i	0.885739	+	0.464183i	$0.153652\pi$
$360$	−6.38167	+	12.6471i	−0.336344	+	0.666563i
$361$	5.48150	+	9.49423i	0.288500	+	0.499696i
$362$	2.07800	+	5.70927i	0.109218	+	0.300073i
$363$	2.25985	+	0.664986i	0.118611	+	0.0349027i
$364$	−0.404312	+	0.339258i	−0.0211917	+	0.0177819i
$365$	3.19284	+	0.222201i	0.167121	+	0.0116305i
$366$	6.42824	−	21.8453i	0.336009	−	1.14187i
$367$	−1.69337	−	4.65249i	−0.0883931	−	0.242858i	0.887617	−	0.460582i	$-0.152359\pi$
$367$	−1.69337	−	4.65249i	−0.0883931	−	0.242858i	−0.976011	+	0.217723i	$0.930137\pi$
$368$	28.5336	−	16.4739i	1.48742	−	0.858760i
$369$	5.13336	+	16.5773i	0.267232	+	0.862980i
$370$	−4.77716	−	16.6391i	−0.248353	−	0.865025i
$371$	1.76911	−	10.0331i	0.0918474	−	0.520893i
$372$	1.13657	+	0.837866i	0.0589285	+	0.0434413i
$373$	−5.91918	+	16.2628i	−0.306484	+	0.842057i	0.686852	+	0.726798i	$0.258992\pi$
$373$	−5.91918	+	16.2628i	−0.306484	+	0.842057i	−0.993335	+	0.115260i	$0.963230\pi$
$374$	−5.19594	−	29.4676i	−0.268676	−	1.52374i
$375$	−17.9976	+	7.14752i	−0.929391	+	0.369097i
$376$	−10.0903	−	8.46673i	−0.520365	−	0.436638i
$377$		−	5.56825i		−	0.286779i
$378$	6.71841	−	8.24012i	0.345558	−	0.423826i
$379$	−8.91774			−0.458073			−0.229037	−	0.973418i	$-0.573558\pi$
$379$	−8.91774			−0.458073			−0.229037	+	0.973418i	$0.573558\pi$
$380$	−4.53547	+	0.478218i	−0.232664	+	0.0245321i
$381$	−0.930389	−	14.7763i	−0.0476653	−	0.757012i
$382$	−6.17043	+	1.08801i	−0.315707	+	0.0556676i
$383$	8.44098	−	23.1914i	0.431314	−	1.18502i	−0.513693	−	0.857974i	$-0.671723\pi$
$383$	8.44098	−	23.1914i	0.431314	−	1.18502i	0.945007	−	0.327051i	$-0.106055\pi$
$384$	−9.31447	−	21.3171i	−0.475327	−	1.08783i
$385$	−7.88926	+	5.73589i	−0.402074	+	0.292328i
$386$	−7.49755	+	12.9861i	−0.381615	+	0.660977i
$387$	−6.47892	−	0.316220i	−0.329342	−	0.0160744i
$388$	−8.63492	+	4.98537i	−0.438372	+	0.253094i
$389$	−6.71441	+	2.44385i	−0.340434	+	0.123908i	−0.506579	−	0.862193i	$-0.669090\pi$
$389$	−6.71441	+	2.44385i	−0.340434	+	0.123908i	0.166145	+	0.986101i	$0.446868\pi$
$390$	−3.25785	−	1.90970i	−0.164968	−	0.0967013i
$391$	−26.4695	+	22.2106i	−1.33862	+	1.12324i
$392$	7.41211	+	8.83341i	0.374368	+	0.446155i
$393$	−12.1481	+	11.5696i	−0.612790	+	0.583611i
$394$	−10.4473	+	3.80249i	−0.526325	+	0.191567i
$395$	2.74982	+	0.684637i	0.138358	+	0.0344478i
$396$	7.52797	−	0.951772i	0.378295	−	0.0478284i
$397$	3.87921	+	2.23966i	0.194692	+	0.112405i	0.594177	−	0.804334i	$-0.297478\pi$
$397$	3.87921	+	2.23966i	0.194692	+	0.112405i	−0.399485	+	0.916740i	$0.630811\pi$
$398$	17.2238	+	3.03702i	0.863352	+	0.152232i
$399$	−6.05458	−	0.678822i	−0.303108	−	0.0339836i
$400$	7.58827	−	23.4071i	0.379413	−	1.17036i
$401$	0.799427	+	4.53377i	0.0399215	+	0.226406i	0.998241	−	0.0592942i	$-0.0188850\pi$
$401$	0.799427	+	4.53377i	0.0399215	+	0.226406i	−0.958319	+	0.285700i	$0.907774\pi$
$402$	6.95959	+	10.4739i	0.347113	+	0.522390i
$403$	0.430668	−	0.513250i	0.0214531	−	0.0255668i
$404$	−8.49220			−0.422503
$405$	18.9621	+	6.74073i	0.942236	+	0.334950i
$406$	−19.2692			−0.956313
$407$	10.6092	−	12.6435i	0.525878	−	0.626717i
$408$	10.4475	+	15.7230i	0.517228	+	0.778406i
$409$	−2.13917	−	12.1318i	−0.105775	−	0.599880i	−0.990908	−	0.134542i	$-0.957044\pi$
$409$	−2.13917	−	12.1318i	−0.105775	−	0.599880i	0.885133	−	0.465339i	$-0.154067\pi$
$410$	−9.35703	−	19.1686i	−0.462111	−	0.946670i
$411$	25.4747	+	2.85615i	1.25657	+	0.140883i
$412$	−1.73510	−	0.305945i	−0.0854823	−	0.0150728i
$413$	−14.5202	−	8.38323i	−0.714491	−	0.412512i
$414$	−20.0278	−	26.3801i	−0.984312	−	1.29651i
$415$	−0.825748	+	3.31658i	−0.0405344	+	0.162805i
$416$	2.16246	−	0.787071i	0.106023	−	0.0385893i
$417$	3.42880	−	3.26553i	0.167909	−	0.159914i
$418$	−10.5649	−	12.5907i	−0.516744	−	0.615832i
$419$	−12.8029	+	10.7429i	−0.625462	+	0.524825i	−0.899515	−	0.436890i	$-0.856080\pi$
$419$	−12.8029	+	10.7429i	−0.625462	+	0.524825i	0.274053	+	0.961715i	$0.411636\pi$
$420$	−1.74832	+	2.98255i	−0.0853094	+	0.145534i
$421$	7.93497	−	2.88809i	0.386727	−	0.140757i	−0.141338	−	0.989961i	$-0.545140\pi$
$421$	7.93497	−	2.88809i	0.386727	−	0.140757i	0.528064	+	0.849205i	$0.322918\pi$
$422$	−25.5070	+	14.7265i	−1.24166	+	0.716875i
$423$	−10.1350	+	15.7300i	−0.492783	+	0.764818i
$424$	−8.66975	+	15.0164i	−0.421040	+	0.729263i
$425$	−3.57449	+	25.5569i	−0.173388	+	1.23969i
$426$	7.86338	+	17.9961i	0.380982	+	0.871914i
$427$	−3.38323	+	9.29536i	−0.163726	+	0.449834i
$428$	4.84578	−	0.854441i	0.234229	−	0.0413010i
$429$	−0.226253	−	3.59331i	−0.0109236	−	0.173487i
$430$	7.92906	−	0.836038i	0.382373	−	0.0403173i
$431$	−11.6530			−0.561306			−0.280653	−	0.959809i	$-0.590551\pi$
$431$	−11.6530			−0.561306			−0.280653	+	0.959809i	$0.590551\pi$
$432$	−21.9631	+	13.0971i	−1.05670	+	0.630136i
$433$		−	10.8242i		−	0.520178i	−0.965585	−	0.260089i	$-0.916248\pi$
$433$		−	10.8242i		−	0.520178i	0.965585	−	0.260089i	$-0.0837519\pi$
$434$	−1.77612	−	1.49034i	−0.0852567	−	0.0715388i
$435$	−12.2483	−	34.3557i	−0.587262	−	1.64723i
$436$	−2.34795	−	13.3159i	−0.112446	−	0.637716i
$437$	−6.49152	+	17.8353i	−0.310531	+	0.853178i
$438$	3.29076	+	2.42590i	0.157239	+	0.115914i
$439$	−4.86673	+	27.6006i	−0.232276	+	1.31731i	0.615998	+	0.787748i	$0.288753\pi$
$439$	−4.86673	+	27.6006i	−0.232276	+	1.31731i	−0.848274	+	0.529557i	$0.822358\pi$
$440$	15.9565	−	4.58117i	0.760694	−	0.218399i
$441$	11.1291	−	12.0207i	0.529956	−	0.572416i
$442$	−4.35811	+	2.51615i	−0.207294	+	0.119681i
$443$	−9.57265	−	26.3006i	−0.454810	−	1.24958i	−0.929302	−	0.369321i	$-0.879590\pi$
$443$	−9.57265	−	26.3006i	−0.454810	−	1.24958i	0.474491	−	0.880260i	$-0.342632\pi$
$444$	1.65142	−	5.61208i	0.0783728	−	0.266337i
$445$	−2.02673	+	29.1225i	−0.0960764	+	1.38054i
$446$	−24.6463	+	20.6807i	−1.16704	+	0.979260i
$447$	−32.3741	−	9.52645i	−1.53124	−	0.450586i
$448$	1.45315	+	3.99251i	0.0686551	+	0.188628i
$449$	−12.5470	−	21.7321i	−0.592130	−	1.02560i	−0.993945	−	0.109878i	$-0.964954\pi$
$449$	−12.5470	−	21.7321i	−0.592130	−	1.02560i	0.401815	−	0.915721i	$-0.368379\pi$
$450$	−24.3014	−	4.61651i	−1.14558	−	0.217624i
$451$	10.1685	−	17.6123i	0.478815	−	0.829333i
$452$	9.77675	+	1.72391i	0.459860	+	0.0810857i
$453$	−19.1493	−	14.1166i	−0.899714	−	0.663256i
$454$	−5.70136	−	2.07512i	−0.267578	−	0.0973904i
$455$	1.36028	+	0.916864i	0.0637709	+	0.0429832i
$456$	9.28813	+	4.61009i	0.434956	+	0.215887i
$457$	−10.7750	+	12.8412i	−0.504036	+	0.600686i	−0.956729	−	0.290980i	$-0.906019\pi$
$457$	−10.7750	+	12.8412i	−0.504036	+	0.600686i	0.452694	+	0.891666i	$0.350463\pi$
$458$		−	7.15325i		−	0.334249i
$459$	20.2985	−	17.5265i	0.947451	−	0.818067i
$460$	7.74990	+	7.47903i	0.361341	+	0.348711i
$461$	19.8382	+	16.6462i	0.923956	+	0.775291i	0.974722	−	0.223419i	$-0.0717219\pi$
$461$	19.8382	+	16.6462i	0.923956	+	0.775291i	−0.0507663	+	0.998711i	$0.516166\pi$
$462$	−12.4348	+	0.782959i	−0.578520	+	0.0364265i
$463$	−17.0551	+	3.00727i	−0.792616	+	0.139760i	−0.555275	−	0.831667i	$-0.687387\pi$
$463$	−17.0551	+	3.00727i	−0.792616	+	0.139760i	−0.237341	+	0.971426i	$0.576276\pi$
$464$	43.5511	+	15.8513i	2.02181	+	0.735878i
$465$	1.52821	−	4.11404i	0.0708691	−	0.190784i
$466$	2.25878	−	12.8102i	0.104636	−	0.593420i
$467$	10.7327	+	6.19652i	0.496649	+	0.286741i	0.727329	−	0.686289i	$-0.240762\pi$
$467$	10.7327	+	6.19652i	0.496649	+	0.286741i	−0.230679	+	0.973030i	$0.574095\pi$
$468$	−0.583431	−	1.13495i	−0.0269691	−	0.0524632i
$469$	−2.73135	−	4.73083i	−0.126122	−	0.218449i
$470$	9.34804	−	21.0148i	0.431193	−	0.969340i
$471$	19.8995	−	4.81526i	0.916921	−	0.221875i
$472$	18.3426	+	21.8599i	0.844288	+	1.00618i
$473$	4.88625	+	5.82321i	0.224670	+	0.267751i
$474$	2.49638	+	2.62119i	0.114663	+	0.120395i
$475$	5.31870	+	13.1391i	0.244039	+	0.602864i
$476$	2.30353	+	3.98983i	0.105582	+	0.182874i
$477$	22.7092	+	9.54337i	1.03978	+	0.436961i
$478$	40.7774	+	23.5429i	1.86512	+	1.07682i
$479$	3.96462	−	22.4845i	0.181148	−	1.02734i	−0.749657	−	0.661826i	$-0.769782\pi$
$479$	3.96462	−	22.4845i	0.181148	−	1.02734i	0.930805	−	0.365515i	$-0.119107\pi$
$480$	11.6109	−	9.61287i	0.529964	−	0.438766i
$481$	−2.60840	−	0.949380i	−0.118933	−	0.0432880i
$482$	21.3728	−	3.76860i	0.973503	−	0.171655i
$483$	7.96273	+	11.9836i	0.362317	+	0.545271i
$484$	−0.749542	−	0.628940i	−0.0340701	−	0.0285882i
$485$	22.2995	+	21.5201i	1.01257	+	0.977177i
$486$	15.8316	+	20.2530i	0.718134	+	0.918695i
$487$		−	3.22215i		−	0.146009i	−0.997332	−	0.0730047i	$-0.976741\pi$
$487$		−	3.22215i		−	0.146009i	0.997332	−	0.0730047i	$-0.0232588\pi$
$488$	10.8218	−	12.8970i	0.489881	−	0.583818i
$489$	−19.4063	+	12.8949i	−0.877583	+	0.583128i
$490$	−11.2540	+	16.6966i	−0.508402	+	0.754277i
$491$	24.5814	+	8.94691i	1.10934	+	0.403768i	0.830753	−	0.556641i	$-0.187910\pi$
$491$	24.5814	+	8.94691i	1.10934	+	0.403768i	0.278591	+	0.960410i	$0.410132\pi$
$492$	0.803132	−	7.16333i	0.0362080	−	0.322948i
$493$	−47.8665	−	8.44015i	−2.15580	−	0.380125i
$494$	−1.38210	+	2.39387i	−0.0621836	+	0.107705i
$495$	−9.30007	−	21.6728i	−0.418007	−	0.974120i
$496$	2.78830	+	4.82948i	0.125198	+	0.216850i
$497$	−2.91784	−	8.01669i	−0.130883	−	0.359598i
$498$	−3.16145	+	3.01091i	−0.141668	+	0.134922i
$499$	26.2418	−	22.0195i	1.17474	−	0.985727i	0.174745	−	0.984614i	$-0.444090\pi$
$499$	26.2418	−	22.0195i	1.17474	−	0.985727i	0.999999	−	0.00111367i	$-0.000354492\pi$
$500$	8.03889	+	0.272713i	0.359510	+	0.0121961i
$501$	4.35707	−	1.05432i	0.194660	−	0.0471034i
$502$	−15.2861	−	41.9983i	−0.682253	−	1.87447i
$503$	13.7378	−	7.93150i	0.612537	−	0.353648i	−0.161421	−	0.986886i	$-0.551608\pi$
$503$	13.7378	−	7.93150i	0.612537	−	0.353648i	0.773958	+	0.633237i	$0.218274\pi$
$504$	6.99091	−	3.59373i	0.311400	−	0.160077i
$505$	7.28375	+	25.3697i	0.324122	+	1.12894i
$506$	−6.74011	+	38.2250i	−0.299634	+	1.69931i
$507$	20.0781	−	8.77311i	0.891700	−	0.389628i
$508$	−2.10332	+	5.77883i	−0.0933198	+	0.256394i
$509$	−2.38054	−	13.5007i	−0.105516	−	0.598410i	−0.991013	−	0.133765i	$-0.957293\pi$
$509$	−2.38054	−	13.5007i	−0.105516	−	0.598410i	0.885497	−	0.464645i	$-0.153818\pi$
$510$	−21.3545	+	25.1109i	−0.945594	+	1.11193i
$511$	−1.36046	−	1.14156i	−0.0601830	−	0.0504995i
$512$		−	1.63110i		−	0.0720849i
$513$	4.84240	−	13.9122i	0.213797	−	0.614240i
$514$	−3.12079			−0.137652
$515$	0.574211	+	5.44587i	0.0253027	+	0.239974i
$516$	2.41340	+	1.19787i	0.106244	+	0.0527333i
$517$	21.5957	−	3.80791i	0.949779	−	0.167472i
$518$	−3.28537	+	9.02649i	−0.144351	+	0.396601i
$519$	−17.0027	+	23.0644i	−0.746337	+	1.01241i
$520$	−1.64182	−	2.25820i	−0.0719988	−	0.0990287i
$521$	13.9166	−	24.1042i	0.609697	−	1.05603i	−0.381593	−	0.924330i	$-0.624625\pi$
$521$	13.9166	−	24.1042i	0.609697	−	1.05603i	0.991290	−	0.131696i	$-0.0420422\pi$
$522$	10.3174	−	45.4335i	0.451583	−	1.98857i
$523$	−7.94269	+	4.58572i	−0.347310	+	0.200519i	−0.663500	−	0.748177i	$-0.730930\pi$
$523$	−7.94269	+	4.58572i	−0.347310	+	0.200519i	0.316190	+	0.948696i	$0.397596\pi$
$524$	6.54791	−	2.38325i	0.286047	−	0.104113i
$525$	10.4096	+	2.66482i	0.454314	+	0.116302i
$526$	26.5821	−	22.3050i	1.15903	−	0.972545i
$527$	−3.75927	−	4.48012i	−0.163756	−	0.195157i
$528$	28.7486	+	8.45959i	1.25112	+	0.368156i
$529$	20.5063	−	7.46369i	0.891579	−	0.324508i
$530$	−29.3805	−	7.31503i	−1.27621	−	0.317745i
$531$	27.5409	−	29.7475i	1.19518	−	1.29093i
$532$	2.19158	+	1.26531i	0.0950170	+	0.0548581i
$533$	−3.36830	−	0.593923i	−0.145897	−	0.0257257i
$534$	−22.1271	+	30.0156i	−0.957533	+	1.29890i
$535$	−6.70878	−	13.7435i	−0.290046	−	0.594182i
$536$	1.61447	+	9.15611i	0.0697345	+	0.395484i
$537$	0.934584	−	1.88294i	0.0403303	−	0.0812550i
$538$	−1.12920	+	1.34572i	−0.0486832	+	0.0580183i
$539$	−19.1974			−0.826892
$540$	−6.09625	−	5.71923i	−0.262341	−	0.246116i
$541$	25.6800			1.10407			0.552035	−	0.833821i	$-0.313852\pi$
$541$	25.6800			1.10407			0.552035	+	0.833821i	$0.313852\pi$
$542$	5.64650	−	6.72923i	0.242538	−	0.289045i
$543$	6.36879	−	0.401012i	0.273311	−	0.0172091i
$544$	−3.48814	−	19.7822i	−0.149553	−	0.848155i
$545$	−37.7662	+	18.4353i	−1.61773	+	0.789682i
$546$	0.838997	+	1.92013i	0.0359058	+	0.0821738i
$547$	38.7852	+	6.83888i	1.65834	+	0.292409i	0.922858	−	0.385140i	$-0.125847\pi$
$547$	38.7852	+	6.83888i	1.65834	+	0.292409i	0.735477	+	0.677549i	$0.236958\pi$
$548$	−9.22108	−	5.32379i	−0.393905	−	0.227421i
$549$	−20.1054	−	12.9542i	−0.858079	−	0.552872i
$550$	15.3776	+	24.5731i	0.655705	+	1.04780i
$551$	−25.0881	+	9.13133i	−1.06879	+	0.389008i
$552$	−5.75930	−	23.8009i	−0.245132	−	1.01303i
$553$	−1.01073	−	1.20454i	−0.0429806	−	0.0512222i
$554$	−21.7004	+	18.2088i	−0.921962	+	0.773618i
$555$	−18.1820	−	0.119990i	−0.771782	−	0.00509330i
$556$	−1.84815	+	0.672672i	−0.0783790	+	0.0285276i
$557$	3.57754	−	2.06550i	0.151585	−	0.0875178i	−0.422289	−	0.906461i	$-0.638773\pi$
$557$	3.57754	−	2.06550i	0.151585	−	0.0875178i	0.573874	+	0.818944i	$0.305440\pi$
$558$	4.46499	−	3.38982i	0.189018	−	0.143503i
$559$	0.639222	−	1.10716i	0.0270362	−	0.0468281i
$560$	−11.0435	+	8.02914i	−0.466671	+	0.339293i
$561$	−31.2322	−	3.50167i	−1.31862	−	0.147840i
$562$	7.01647	−	19.2776i	0.295972	−	0.813176i
$563$	−17.1381	+	3.02191i	−0.722286	+	0.127358i	−0.522694	−	0.852521i	$-0.675073\pi$
$563$	−17.1381	+	3.02191i	−0.722286	+	0.127358i	−0.199592	+	0.979879i	$0.563962\pi$
$564$	6.47362	−	4.30153i	0.272589	−	0.181127i
$565$	−3.23550	−	30.6858i	−0.136118	−	1.29096i
$566$	34.1610			1.43590
$567$	−6.31076	−	9.21266i	−0.265027	−	0.386895i
$568$			14.5199i			0.609239i
$569$	−3.52883	−	2.96104i	−0.147936	−	0.124133i	0.565816	−	0.824532i	$-0.308561\pi$
$569$	−3.52883	−	2.96104i	−0.147936	−	0.124133i	−0.713752	+	0.700398i	$0.753006\pi$
$570$	−3.26175	+	17.8102i	−0.136620	+	0.745986i
$571$	−2.79686	−	15.8618i	−0.117045	−	0.663794i	−0.985717	−	0.168407i	$-0.946138\pi$
$571$	−2.79686	−	15.8618i	−0.117045	−	0.663794i	0.868673	−	0.495386i	$-0.164974\pi$
$572$	−0.511488	+	1.40530i	−0.0213864	+	0.0587586i
$573$	−0.733238	+	6.53993i	−0.0306315	+	0.273209i
$574$	−2.05530	+	11.6562i	−0.0857864	+	0.486519i
$575$	15.6958	−	29.5669i	0.654561	−	1.23302i
$576$	−10.1918	+	1.28856i	−0.424656	+	0.0536899i
$577$	23.9756	−	13.8423i	0.998116	−	0.576262i	0.0904254	−	0.995903i	$-0.471177\pi$
$577$	23.9756	−	13.8423i	0.998116	−	0.576262i	0.907690	+	0.419641i	$0.137844\pi$
$578$	5.43556	+	14.9341i	0.226089	+	0.621176i
$579$	10.8618	+	11.4049i	0.451403	+	0.473972i
$580$	−1.05179	+	15.1134i	−0.0436733	+	0.627549i
$581$	1.45281	−	1.21905i	0.0602726	−	0.0505748i
$582$	9.31017	+	38.4752i	0.385919	+	1.59485i
$583$	−9.87317	−	27.1263i	−0.408905	−	1.12346i
$584$	1.51131	+	2.61766i	0.0625384	+	0.108320i
$585$	−2.89016	+	2.71639i	−0.119493	+	0.112309i
$586$	−5.15817	+	8.93422i	−0.213082	+	0.369069i
$587$	−16.8114	−	2.96430i	−0.693880	−	0.122350i	−0.184424	−	0.982847i	$-0.559042\pi$
$587$	−16.8114	−	2.96430i	−0.693880	−	0.122350i	−0.509455	+	0.860497i	$0.670153\pi$
$588$	−6.23508	+	2.72441i	−0.257130	+	0.112353i
$589$	−3.01873	−	1.09873i	−0.124385	−	0.0452723i
$590$	−27.8500	+	41.3189i	−1.14657	+	1.70107i
$591$	0.733801	+	11.6541i	0.0301845	+	0.479385i
$592$	14.8508	−	17.6985i	0.610366	−	0.727405i
$593$		−	7.85373i		−	0.322514i	−0.986912	−	0.161257i	$-0.948445\pi$
$593$		−	7.85373i		−	0.322514i	0.986912	−	0.161257i	$-0.0515548\pi$
$594$	4.81198	−	29.7385i	0.197438	−	1.22018i
$595$	9.94353	−	10.3037i	0.407645	−	0.422409i
$596$	10.7378	+	9.01007i	0.439837	+	0.369067i
$597$	8.16694	−	16.4543i	0.334251	−	0.673428i
$598$	6.42867	−	1.13355i	0.262888	−	0.0463543i
$599$	45.0491	+	16.3965i	1.84066	+	0.669944i	0.989404	+	0.145188i	$0.0463787\pi$
$599$	45.0491	+	16.3965i	1.84066	+	0.669944i	0.851253	+	0.524756i	$0.175843\pi$
$600$	−15.0972	−	10.3215i	−0.616343	−	0.421373i
$601$	4.31451	−	24.4688i	0.175993	−	0.998104i	−0.760999	−	0.648753i	$-0.775291\pi$
$601$	4.31451	−	24.4688i	0.175993	−	0.998104i	0.936992	−	0.349351i	$-0.113598\pi$
$602$	−3.83139	−	2.21206i	−0.156156	−	0.0901567i
$603$	12.6170	−	3.90700i	0.513804	−	0.159105i
$604$	4.94082	+	8.55775i	0.201039	+	0.348210i
$605$	−1.23602	+	2.77863i	−0.0502514	+	0.112967i
$606$	−9.51765	+	32.3442i	−0.386628	+	1.31389i
$607$	−28.6468	−	34.1399i	−1.16274	−	1.38570i	−0.908148	−	0.418648i	$-0.862504\pi$
$607$	−28.6468	−	34.1399i	−1.16274	−	1.38570i	−0.254590	−	0.967049i	$-0.581940\pi$
$608$	−7.09240	−	8.45239i	−0.287635	−	0.342790i
$609$	−5.71327	+	19.4156i	−0.231513	+	0.786761i
$610$	26.8603	+	11.9483i	1.08754	+	0.483772i
$611$	−1.84400	−	3.19389i	−0.0746001	−	0.129211i
$612$	−10.6408	+	3.29504i	−0.430128	+	0.133194i
$613$	−5.10015	−	2.94457i	−0.205993	−	0.118930i	0.393455	−	0.919344i	$-0.371280\pi$
$613$	−5.10015	−	2.94457i	−0.205993	−	0.118930i	−0.599448	+	0.800414i	$0.704613\pi$
$614$	5.22571	−	29.6365i	0.210893	−	1.19603i
$615$	−22.0887	+	3.74470i	−0.890700	+	0.151001i
$616$	−8.65617	−	3.15059i	−0.348767	−	0.126941i
$617$	−30.2359	+	5.33141i	−1.21725	+	0.214635i	−0.745143	−	0.666905i	$-0.767619\pi$
$617$	−30.2359	+	5.33141i	−1.21725	+	0.214635i	−0.472110	+	0.881539i	$0.656508\pi$
$618$	−3.10987	+	6.26559i	−0.125097	+	0.252039i
$619$	34.9350	+	29.3139i	1.40416	+	1.17823i	0.959219	+	0.282666i	$0.0912187\pi$
$619$	34.9350	+	29.3139i	1.40416	+	1.17823i	0.444938	+	0.895561i	$0.353226\pi$
$620$	−1.26587	+	1.31172i	−0.0508385	+	0.0526798i
$621$	−32.5188	+	12.3584i	−1.30494	+	0.495924i
$622$		−	7.80060i		−	0.312776i
$623$	10.4124	−	12.4090i	0.417162	−	0.497155i
$624$	−0.316711	−	5.02994i	−0.0126786	−	0.201359i
$625$	−6.08024	−	24.2493i	−0.243209	−	0.969974i
$626$	−53.6846	−	19.5396i	−2.14567	−	0.780960i
$627$	−15.8189	+	6.91204i	−0.631745	+	0.276040i
$628$	−8.37491	−	1.47672i	−0.334195	−	0.0589277i
$629$	−12.1149	+	20.9836i	−0.483053	+	0.836672i
$630$	9.40020	+	10.0015i	0.374513	+	0.398471i
$631$	−6.80759	−	11.7911i	−0.271006	−	0.469396i	0.698114	−	0.715987i	$-0.254023\pi$
$631$	−6.80759	−	11.7911i	−0.271006	−	0.469396i	−0.969120	+	0.246591i	$0.920690\pi$
$632$	0.915317	+	2.51481i	0.0364094	+	0.100034i
$633$	7.27564	+	30.0673i	0.289181	+	1.19507i
$634$	1.30271	−	1.09310i	0.0517371	−	0.0434126i
$635$	19.0677	+	1.32699i	0.756680	+	0.0526600i
$636$	−7.05633	−	7.40913i	−0.279802	−	0.293791i
$637$	1.10425	+	3.03391i	0.0437520	+	0.120208i
$638$	−47.2841	+	27.2995i	−1.87199	+	1.08080i
$639$	20.4644	−	2.58734i	0.809558	−	0.102354i
$640$	28.8665	−	8.28770i	1.14105	−	0.327600i
$641$	1.38566	−	7.85848i	0.0547304	−	0.310391i	−0.945137	−	0.326674i	$-0.894072\pi$
$641$	1.38566	−	7.85848i	0.0547304	−	0.310391i	0.999867	+	0.0162827i	$0.00518316\pi$
$642$	2.17661	−	19.4137i	0.0859039	−	0.766198i
$643$	−5.16505	+	14.1909i	−0.203690	+	0.559633i	−0.998909	−	0.0466885i	$-0.985133\pi$
$643$	−5.16505	+	14.1909i	−0.203690	+	0.559633i	0.795220	+	0.606321i	$0.207355\pi$
$644$	−1.03776	−	5.88543i	−0.0408935	−	0.231918i
$645$	1.50856	−	8.23721i	0.0593995	−	0.324340i
$646$	18.4835	+	15.5095i	0.727225	+	0.610214i
$647$			44.8366i			1.76271i	0.472455	+	0.881355i	$0.343368\pi$
$647$			44.8366i			1.76271i	−0.472455	+	0.881355i	$0.656632\pi$
$648$	4.73022	+	18.4077i	0.185821	+	0.723121i
$649$	−47.5075			−1.86483
$650$	2.99892	−	3.84370i	0.117627	−	0.150762i
$651$	−2.02829	+	1.34774i	−0.0794950	+	0.0528221i
$652$	9.53092	−	1.68056i	0.373260	−	0.0658157i
$653$	−6.37556	+	17.5167i	−0.249495	+	0.685482i	0.750210	+	0.661199i	$0.229952\pi$
$653$	−6.37556	+	17.5167i	−0.249495	+	0.685482i	−0.999705	+	0.0242823i	$0.992270\pi$
$654$	−53.3477	−	5.98119i	−2.08606	−	0.233883i
$655$	−12.7359	−	17.5172i	−0.497632	−	0.684453i
$656$	14.2339	−	24.6539i	0.555742	−	0.962573i
$657$	3.42005	−	2.59650i	0.133429	−	0.101299i
$658$	−11.0526	+	6.38123i	−0.430876	+	0.248766i
$659$	−8.86949	+	3.22823i	−0.345506	+	0.125754i	−0.508944	−	0.860800i	$-0.669964\pi$
$659$	−8.86949	+	3.22823i	−0.345506	+	0.125754i	0.163438	+	0.986554i	$0.447742\pi$
$660$	−0.0646460	+	9.79573i	−0.00251634	+	0.381298i
$661$	−21.0425	+	17.6567i	−0.818457	+	0.686767i	−0.952610	−	0.304194i	$-0.901613\pi$
$661$	−21.0425	+	17.6567i	−0.818457	+	0.686767i	0.134153	+	0.990961i	$0.457169\pi$
$662$	13.4565	+	16.0369i	0.523003	+	0.623291i
$663$	1.24311	+	5.13727i	0.0482784	+	0.199515i
$664$	−3.03314	+	1.10397i	−0.117709	+	0.0428425i
$665$	1.90028	−	7.63239i	0.0736897	−	0.295972i
$666$	−19.5239	−	12.5795i	−0.756534	−	0.487446i
$667$	54.6026	+	31.5248i	2.11422	+	1.22065i
$668$	−1.83372	−	0.323334i	−0.0709486	−	0.0125102i
$669$	13.5303	+	30.9654i	0.523112	+	1.19719i
$670$	−14.5892	+	7.12163i	−0.563631	+	0.275133i
$671$	4.86712	+	27.6028i	0.187893	+	1.06559i
$672$	−8.34774	+	0.525616i	−0.322021	+	0.0202761i
$673$	17.1645	−	20.4558i	0.661642	−	0.788514i	−0.325979	−	0.945377i	$-0.605694\pi$
$673$	17.1645	−	20.4558i	0.661642	−	0.788514i	0.987620	+	0.156863i	$0.0501382\pi$
$674$	15.3210			0.590144
$675$	−11.8569	+	23.1174i	−0.456374	+	0.889788i
$676$	−9.10112			−0.350043
$677$	21.7428	−	25.9121i	0.835645	−	0.995883i	−0.164310	−	0.986409i	$-0.552540\pi$
$677$	21.7428	−	25.9121i	0.835645	−	0.995883i	0.999955	−	0.00947415i	$-0.00301576\pi$
$678$	17.5232	−	35.3046i	0.672973	−	1.35587i
$679$	−2.98604	−	16.9347i	−0.114594	−	0.649894i
$680$	−21.9009	+	10.6908i	−0.839859	+	0.409972i
$681$	−3.78134	+	5.12942i	−0.144901	+	0.196560i
$682$	−6.46982	−	1.14080i	−0.247742	−	0.0436836i
$683$	15.0388	+	8.68268i	0.575445	+	0.332233i	0.759321	−	0.650716i	$-0.225531\pi$
$683$	15.0388	+	8.68268i	0.575445	+	0.332233i	−0.183876	+	0.982949i	$0.558864\pi$
$684$	−4.15684	+	4.48989i	−0.158941	+	0.171675i
$685$	−7.99544	+	32.1133i	−0.305490	+	1.22699i
$686$	23.9579	−	8.71998i	0.914718	−	0.332930i
$687$	−7.20762	−	2.12093i	−0.274988	−	0.0809183i
$688$	6.83981	+	8.15137i	0.260765	+	0.310768i
$689$	−3.71905	+	3.12066i	−0.141685	+	0.118888i
$690$	37.1711	−	21.1349i	1.41508	−	0.804592i
$691$	−13.7800	+	5.01549i	−0.524214	+	0.190798i	−0.590553	−	0.806999i	$-0.701090\pi$
$691$	−13.7800	+	5.01549i	−0.524214	+	0.190798i	0.0663389	+	0.997797i	$0.478868\pi$
$692$	10.3074	−	5.95096i	0.391827	−	0.226222i
$693$	−2.89799	+	12.7615i	−0.110085	+	0.484768i
$694$	20.7216	−	35.8909i	0.786582	−	1.36240i
$695$	3.59470	+	4.94423i	0.136355	+	0.187545i
$696$	20.4394	−	27.7263i	0.774755	−	1.05096i
$697$	−10.2111	+	28.0548i	−0.386773	+	1.06265i
$698$	3.88958	−	0.685839i	0.147223	−	0.0259594i
$699$	−12.2378	−	6.07415i	−0.462877	−	0.229745i
$700$	−3.51890	−	2.74550i	−0.133002	−	0.103770i
$701$	−28.8893			−1.09113			−0.545567	−	0.838067i	$-0.683686\pi$
$701$	−28.8893			−1.09113			−0.545567	+	0.838067i	$0.683686\pi$
$702$	−4.97657	+	0.950109i	−0.187829	+	0.0358596i
$703$			13.3092i			0.501966i
$704$	9.22221	+	7.73836i	0.347575	+	0.291650i
$705$	−18.4029	−	15.6499i	−0.693092	−	0.589411i
$706$	−3.66652	−	20.7939i	−0.137991	−	0.782588i
$707$	5.00922	−	13.7627i	0.188391	−	0.517600i
$708$	−15.4299	+	6.74206i	−0.579889	+	0.253382i
$709$	−0.360524	+	2.04463i	−0.0135398	+	0.0767878i	−0.990829	−	0.135122i	$-0.956857\pi$
$709$	−0.360524	+	2.04463i	−0.0135398	+	0.0767878i	0.977289	+	0.211910i	$0.0679684\pi$
$710$	−24.3694	+	6.99657i	−0.914568	+	0.262577i
$711$	3.38129	−	1.73818i	0.126808	−	0.0651867i
$712$	−23.8762	+	13.7849i	−0.894798	+	0.516612i
$713$	2.59472	+	7.12893i	0.0971730	+	0.266981i
$714$	17.7777	−	4.30184i	0.665316	−	0.160992i
$715$	4.63691	+	0.322699i	0.173411	+	0.0120682i
$716$	−0.668871	+	0.561249i	−0.0249969	+	0.0209749i
$717$	35.8122	−	34.1070i	1.33743	−	1.27375i
$718$	0.873632	+	2.40028i	0.0326037	+	0.0895778i
$719$	9.24248	+	16.0084i	0.344686	+	0.597014i	0.985297	−	0.170852i	$-0.0546519\pi$
$719$	9.24248	+	16.0084i	0.344686	+	0.597014i	−0.640610	+	0.767866i	$0.721319\pi$
$720$	−13.0183	−	30.3378i	−0.485164	−	1.13062i
$721$	1.51929	−	2.63149i	0.0565814	−	0.0980019i
$722$	−17.8041	−	3.13934i	−0.662600	−	0.116834i
$723$	2.53975	−	22.6526i	0.0944542	−	0.842460i
$724$	−2.49076	−	0.906563i	−0.0925684	−	0.0336921i
$725$	46.0520	−	9.82059i	1.71033	−	0.364728i
$726$	−3.23549	+	2.14989i	−0.120080	+	0.0797899i
$727$	−26.3979	+	31.4598i	−0.979045	+	1.16678i	0.00694522	+	0.999976i	$0.497789\pi$
$727$	−26.3979	+	31.4598i	−0.979045	+	1.16678i	−0.985990	+	0.166804i	$0.946655\pi$
$728$			1.54922i			0.0574179i
$729$	25.1010	−	9.94693i	0.929666	−	0.368405i
$730$	−3.66512	+	3.79786i	−0.135652	+	0.140565i
$731$	−8.54864	−	7.17316i	−0.316183	−	0.265309i
$732$	5.49804	+	8.27432i	0.203214	+	0.305828i
$733$	3.29255	−	0.580566i	0.121613	−	0.0214437i	−0.112510	−	0.993651i	$-0.535889\pi$
$733$	3.29255	−	0.580566i	0.121613	−	0.0214437i	0.234123	+	0.972207i	$0.424778\pi$
$734$	7.67229	+	2.79248i	0.283189	+	0.103072i
$735$	13.4868	+	16.2900i	0.497467	+	0.600866i
$736$	−4.52477	+	25.6612i	−0.166785	+	0.945886i
$737$	−13.4048	−	7.73924i	−0.493770	−	0.285078i
$738$	−26.3829	−	11.0872i	−0.971166	−	0.408126i
$739$	9.86291	+	17.0831i	0.362813	+	0.628411i	0.988423	−	0.151726i	$-0.0484830\pi$
$739$	9.86291	+	17.0831i	0.362813	+	0.628411i	−0.625610	+	0.780136i	$0.715150\pi$
$740$	6.90041	+	3.06952i	0.253664	+	0.112838i
$741$	2.00227	+	2.10238i	0.0735554	+	0.0772330i
$742$	10.7992	+	12.8700i	0.396450	+	0.472471i
$743$	14.4345	+	17.2023i	0.529549	+	0.631092i	0.962811	−	0.270176i	$-0.0870820\pi$
$743$	14.4345	+	17.2023i	0.529549	+	0.631092i	−0.433262	+	0.901268i	$0.642638\pi$
$744$	4.02844	−	0.974796i	0.147690	−	0.0357378i
$745$	17.7070	−	39.8061i	0.648734	−	1.45838i
$746$	−14.2698	−	24.7161i	−0.522456	−	0.904921i
$747$	2.09643	+	4.07821i	0.0767045	+	0.149214i
$748$	11.3051	+	6.52702i	0.413357	+	0.238652i
$749$	−1.47360	+	8.35721i	−0.0538442	+	0.305366i
$750$	10.0483	−	30.3120i	0.366911	−	1.10684i
$751$	−23.9497	−	8.71699i	−0.873938	−	0.318088i	−0.134177	−	0.990957i	$-0.542839\pi$
$751$	−23.9497	−	8.71699i	−0.873938	−	0.318088i	−0.739761	+	0.672870i	$0.765061\pi$
$752$	30.2299	−	5.33034i	1.10237	−	0.194378i
$753$	−46.8498	+	2.94990i	−1.70730	+	0.107500i
$754$	7.03415	+	5.90235i	0.256169	+	0.214951i
$755$	21.3278	−	22.1002i	0.776197	−	0.804309i
$756$	0.869822	+	4.55604i	0.0316351	+	0.165701i
$757$		−	43.0981i		−	1.56643i	−0.621753	−	0.783214i	$-0.713579\pi$
$757$		−	43.0981i		−	1.56643i	0.621753	−	0.783214i	$-0.286421\pi$
$758$	9.45282	−	11.2654i	0.343342	−	0.409179i
$759$	36.5172	+	18.1250i	1.32549	+	0.657896i
$760$	−7.48206	+	11.1006i	−0.271403	+	0.402660i
$761$	−26.5013	−	9.64570i	−0.960673	−	0.349656i	−0.186376	−	0.982479i	$-0.559674\pi$
$761$	−26.5013	−	9.64570i	−0.960673	−	0.349656i	−0.774297	+	0.632822i	$0.781896\pi$
$762$	19.6525	+	14.4876i	0.711935	+	0.524829i
$763$	22.9651	+	4.04937i	0.831393	+	0.146597i
$764$	1.36674	−	2.36726i	0.0494469	−	0.0856445i
$765$	18.9702	+	28.9622i	0.685869	+	1.04713i
$766$	20.3493	+	35.2461i	0.735251	+	1.27349i
$767$	2.73267	+	7.50796i	0.0986711	+	0.271097i
$768$	25.4227	+	7.48092i	0.917363	+	0.269945i
$769$	0.986304	−	0.827608i	0.0355670	−	0.0298443i	−0.624831	−	0.780760i	$-0.714832\pi$
$769$	0.986304	−	0.827608i	0.0355670	−	0.0298443i	0.660398	+	0.750916i	$0.270388\pi$
$770$	1.11671	−	16.0463i	0.0402436	−	0.578267i
$771$	−0.925308	+	3.14451i	−0.0333241	+	0.113247i
$772$	−2.23745	−	6.14733i	−0.0805274	−	0.221247i
$773$	4.24332	−	2.44988i	0.152622	−	0.0881162i	−0.421744	−	0.906715i	$-0.638582\pi$
$773$	4.24332	−	2.44988i	0.152622	−	0.0881162i	0.574366	+	0.818599i	$0.305249\pi$
$774$	7.26714	−	7.84938i	0.261212	−	0.282140i
$775$	5.00437	+	2.65661i	0.179762	+	0.0954283i
$776$	−5.08217	+	28.8224i	−0.182439	+	1.03466i
$777$	8.12099	+	5.98668i	0.291339	+	0.214771i
$778$	4.03007	−	11.0725i	0.144485	−	0.396970i
$779$	2.84770	+	16.1501i	0.102029	+	0.578637i
$780$	1.55181	−	0.553242i	0.0555636	−	0.0198092i
$781$	−18.5176	−	15.5381i	−0.662612	−	0.555997i
$782$		−	56.9812i		−	2.03764i
$783$	−42.7198	−	23.8668i	−1.52668	−	0.852931i
$784$	−26.8727			−0.959739
$785$	2.77158	+	26.2859i	0.0989218	+	0.938183i
$786$	−1.73847	−	27.6101i	−0.0620091	−	0.984818i
$787$	−31.1341	+	5.48979i	−1.10981	+	0.195690i	−0.698363	−	0.715743i	$-0.746088\pi$
$787$	−31.1341	+	5.48979i	−1.10981	+	0.195690i	−0.411448	+	0.911433i	$0.634977\pi$
$788$	1.65890	−	4.55778i	0.0590958	−	0.162364i
$789$	−14.5930	−	33.3975i	−0.519525	−	1.18898i
$790$	−3.77969	+	2.74802i	−0.134475	+	0.0977701i
$791$	−8.56074	+	14.8276i	−0.304385	+	0.527210i
$792$	12.0634	−	18.7229i	0.428655	−	0.665289i
$793$	4.08231	−	2.35692i	0.144967	−	0.0836967i
$794$	−6.94125	+	2.52641i	−0.246336	+	0.0896589i
$795$	−16.0819	+	27.4349i	−0.570366	+	0.973017i
$796$	−5.84498	+	4.90452i	−0.207170	+	0.173836i
$797$	−16.6580	−	19.8522i	−0.590057	−	0.703202i	0.385560	−	0.922683i	$-0.374008\pi$
$797$	−16.6580	−	19.8522i	−0.590057	−	0.703202i	−0.975617	+	0.219480i	$0.929564\pi$
$798$	7.27539	−	6.92896i	0.257546	−	0.245283i
$799$	−30.2508	+	11.0104i	−1.07020	+	0.389520i
$800$	10.3233	+	16.4964i	0.364984	+	0.583235i
$801$	23.6831	+	31.1949i	0.836802	+	1.10222i
$802$	−6.57473	−	3.79592i	−0.232162	−	0.134039i
$803$	−4.95568	−	0.873820i	−0.174882	−	0.0308364i
$804$	−5.45201	−	0.611264i	−0.192278	−	0.0215576i
$805$	−16.6921	+	8.14814i	−0.588319	+	0.287184i
$806$	0.191860	+	1.08809i	0.00675797	+	0.0383264i
$807$	1.02115	+	1.53679i	0.0359461	+	0.0540974i
$808$	−16.0228	+	19.0952i	−0.563680	+	0.671768i
$809$	16.8506			0.592435			0.296217	−	0.955121i	$-0.404275\pi$
$809$	16.8506			0.592435			0.296217	+	0.955121i	$0.404275\pi$
$810$	−28.6152	+	16.8089i	−1.00544	+	0.590606i
$811$	−26.5505			−0.932313			−0.466156	−	0.884702i	$-0.654362\pi$
$811$	−26.5505			−0.932313			−0.466156	+	0.884702i	$0.654362\pi$
$812$	5.40358	−	6.43974i	0.189629	−	0.225991i
$813$	−5.10621	−	7.68462i	−0.179082	−	0.269511i
$814$	4.72633	+	26.8044i	0.165658	+	0.939493i
$815$	−13.1952	−	27.0313i	−0.462207	−	0.946866i
$816$	−43.7191	−	4.90166i	−1.53047	−	0.171592i
$817$	−6.03666	−	1.06443i	−0.211196	−	0.0372396i
$818$	17.5932	+	10.1574i	0.615132	+	0.355146i
$819$	2.18348	−	0.276061i	0.0762970	−	0.00964634i
$820$	9.03009	+	2.24827i	0.315344	+	0.0785131i
$821$	43.6959	−	15.9040i	1.52500	−	0.555054i	0.562608	−	0.826724i	$-0.309798\pi$
$821$	43.6959	−	15.9040i	1.52500	−	0.555054i	0.962390	+	0.271670i	$0.0875760\pi$
$822$	−30.6113	+	29.1536i	−1.06769	+	1.01685i
$823$	0.257495	+	0.306870i	0.00897570	+	0.0106968i	0.770514	−	0.637424i	$-0.220000\pi$
$823$	0.257495	+	0.306870i	0.00897570	+	0.0106968i	−0.761538	+	0.648120i	$0.775555\pi$
$824$	−3.96167	+	3.32424i	−0.138011	+	0.115805i
$825$	29.3193	−	8.20866i	1.02077	−	0.285789i
$826$	25.9816	−	9.45654i	0.904017	−	0.329035i
$827$	−0.954191	+	0.550903i	−0.0331805	+	0.0191568i	−0.516498	−	0.856288i	$-0.672765\pi$
$827$	−0.954191	+	0.550903i	−0.0331805	+	0.0191568i	0.483318	+	0.875445i	$0.339431\pi$
$828$	14.4325	+	0.704416i	0.501565	+	0.0244801i
$829$	−2.63061	+	4.55635i	−0.0913648	+	0.158249i	−0.908086	−	0.418784i	$-0.862456\pi$
$829$	−2.63061	+	4.55635i	−0.0913648	+	0.158249i	0.816721	+	0.577033i	$0.195790\pi$
$830$	−3.31441	−	4.55872i	−0.115045	−	0.158235i
$831$	11.9131	+	27.2642i	0.413260	+	0.945785i
$832$	0.692479	−	1.90257i	0.0240074	−	0.0659597i
$833$	27.7542	−	4.89382i	0.961627	−	0.169561i
$834$	0.490683	+	7.79295i	0.0169910	+	0.269848i
$835$	0.606846	+	5.75539i	0.0210008	+	0.199173i
$836$	7.17047			0.247996
$837$	−2.09173	−	5.50401i	−0.0723006	−	0.190246i
$838$		−	27.5609i		−	0.952075i
$839$	−27.5648	−	23.1296i	−0.951642	−	0.798523i	0.0279310	−	0.999610i	$-0.491108\pi$
$839$	−27.5648	−	23.1296i	−0.951642	−	0.798523i	−0.979573	+	0.201087i	$0.935553\pi$
$840$	3.40778	+	9.55859i	0.117579	+	0.329803i
$841$	10.3649	+	58.7823i	0.357410	+	2.02698i
$842$	−4.76267	+	13.0853i	−0.164132	+	0.450950i
$843$	−17.3437	−	12.7856i	−0.597350	−	0.440358i
$844$	2.23126	−	12.6541i	0.0768033	−	0.435573i
$845$	7.80602	+	27.1888i	0.268535	+	0.935322i
$846$	−9.12791	−	29.4770i	−0.313824	−	1.01344i
$847$	1.46140	−	0.843742i	0.0502145	−	0.0289913i
$848$	−13.8205	−	37.9716i	−0.474599	−	1.30395i
$849$	10.1287	−	34.4207i	0.347616	−	1.18132i
$850$	−28.4961	−	31.6059i	−0.977407	−	1.08407i
$851$	24.0772	−	20.2032i	0.825357	−	0.692557i
$852$	−8.21938	−	2.41865i	−0.281591	−	0.0828615i
$853$	0.137118	+	0.376728i	0.00469483	+	0.0128989i	0.942018	−	0.335563i	$-0.108926\pi$
$853$	0.137118	+	0.376728i	0.00469483	+	0.0128989i	−0.937323	+	0.348462i	$0.886704\pi$
$854$	−8.15623	−	14.1270i	−0.279101	−	0.483416i
$855$	16.9785	+	8.56722i	0.580651	+	0.292993i
$856$	7.22159	−	12.5082i	0.246829	−	0.427520i
$857$	38.0088	+	6.70198i	1.29836	+	0.228935i	0.779757	−	0.626083i	$-0.215343\pi$
$857$	38.0088	+	6.70198i	1.29836	+	0.228935i	0.518599	+	0.855018i	$0.326454\pi$
$858$	4.77912	+	3.52310i	0.163156	+	0.120277i
$859$	16.0641	+	5.84684i	0.548099	+	0.199492i	0.601202	−	0.799097i	$-0.294689\pi$
$859$	16.0641	+	5.84684i	0.548099	+	0.199492i	−0.0531029	+	0.998589i	$0.516911\pi$
$860$	−1.94411	+	2.88433i	−0.0662938	+	0.0983549i
$861$	11.1354	+	5.52695i	0.379493	+	0.188358i
$862$	12.3522	−	14.7208i	0.420719	−	0.501393i
$863$			23.2510i			0.791472i	0.918364	+	0.395736i	$0.129511\pi$
$863$			23.2510i			0.791472i	−0.918364	+	0.395736i	$0.870489\pi$
$864$	3.23038	−	19.9640i	0.109900	−	0.679190i
$865$	−26.6186	−	25.6882i	−0.905058	−	0.873425i
$866$	13.6738	+	11.4737i	0.464654	+	0.389891i
$867$	16.6592	−	1.04895i	0.565777	−	0.0356242i
$868$	0.996144	−	0.175647i	0.0338113	−	0.00596185i
$869$	−4.18672	−	1.52384i	−0.142025	−	0.0516928i
$870$	56.3835	+	20.9443i	1.91158	+	0.710079i
$871$	−0.452035	+	2.56362i	−0.0153166	+	0.0868648i
$872$	−34.3716	−	19.8445i	−1.16397	−	0.672019i
$873$	41.5281	+	2.02688i	1.40551	+	0.0685995i
$874$	−15.6496	−	27.1059i	−0.529356	−	0.916872i
$875$	−5.18379	+	12.8672i	−0.175244	+	0.434991i
$876$	−1.73355	+	0.419482i	−0.0585712	+	0.0141730i
$877$	0.503887	+	0.600510i	0.0170151	+	0.0202778i	0.774485	−	0.632592i	$-0.218009\pi$
$877$	0.503887	+	0.600510i	0.0170151	+	0.0202778i	−0.757470	+	0.652870i	$0.773565\pi$
$878$	−29.7080	−	35.4047i	−1.00260	−	1.19485i
$879$	7.47274	+	7.84636i	0.252049	+	0.264651i
$880$	−15.7240	+	35.3482i	−0.530056	+	1.19159i
$881$	4.60962	+	7.98410i	0.155302	+	0.268991i	0.933169	−	0.359438i	$-0.117032\pi$
$881$	4.60962	+	7.98410i	0.155302	+	0.268991i	−0.777867	+	0.628429i	$0.783698\pi$
$882$	3.38848	+	26.8009i	0.114096	+	0.902434i
$883$	−31.4539	−	18.1599i	−1.05851	−	0.611129i	−0.133488	−	0.991050i	$-0.542618\pi$
$883$	−31.4539	−	18.1599i	−1.05851	−	0.611129i	−0.925019	+	0.379921i	$0.875951\pi$
$884$	0.381232	−	2.16207i	0.0128222	−	0.0727183i
$885$	33.3755	+	40.3126i	1.12190	+	1.35509i
$886$	43.3716	+	15.7860i	1.45710	+	0.530340i
$887$	33.0505	−	5.82770i	1.10973	−	0.195675i	0.411401	−	0.911454i	$-0.365040\pi$
$887$	33.0505	−	5.82770i	1.10973	−	0.195675i	0.698326	+	0.715779i	$0.253928\pi$
$888$	−9.50326	−	14.3020i	−0.318908	−	0.479943i
$889$	−8.12468	−	6.81741i	−0.272493	−	0.228649i
$890$	−34.6410	−	33.4302i	−1.16117	−	1.12058i
$891$	−28.5378	−	13.6660i	−0.956051	−	0.457827i
$892$		−	14.0362i		−	0.469967i
$893$	−11.3664	+	13.5459i	−0.380361	+	0.453296i
$894$	46.3510	−	30.7989i	1.55021	−	1.03007i
$895$	2.25037	+	1.51681i	0.0752216	+	0.0507013i
$896$	−15.6597	−	5.69966i	−0.523154	−	0.190412i
$897$	0.763925	−	6.81363i	0.0255067	−	0.227501i
$898$	40.7531	+	7.18587i	1.35995	+	0.239796i
$899$	−5.33576	+	9.24181i	−0.177958	+	0.308232i
$900$	8.35760	−	6.82693i	0.278587	−	0.227564i
$901$	21.1890	+	36.7004i	0.705907	+	1.22267i
$902$	11.4704	+	31.5146i	0.381921	+	1.04932i
$903$	−3.36487	+	3.20465i	−0.111976	+	0.106644i
$904$	22.3228	−	18.7310i	0.742444	−	0.622985i
$905$	−0.571952	+	8.21848i	−0.0190123	+	0.273192i
$906$	38.1313	−	9.22696i	1.26683	−	0.306545i
$907$	3.34276	+	9.18415i	0.110994	+	0.304955i	0.982737	−	0.185010i	$-0.0592318\pi$
$907$	3.34276	+	9.18415i	0.110994	+	0.304955i	−0.871742	+	0.489965i	$0.837010\pi$
$908$	2.29232	−	1.32347i	0.0760732	−	0.0439209i
$909$	29.7681	+	19.1800i	0.987345	+	0.636160i
$910$	−2.60014	+	0.746511i	−0.0861937	+	0.0247466i
$911$	6.63575	−	37.6332i	0.219852	−	1.24684i	−0.652433	−	0.757847i	$-0.726252\pi$
$911$	6.63575	−	37.6332i	0.219852	−	1.24684i	0.872285	−	0.488998i	$-0.162637\pi$
$912$	−22.1434	+	9.67553i	−0.733241	+	0.320389i
$913$	1.83792	−	5.04965i	0.0608264	−	0.167119i
$914$	−4.80022	−	27.2234i	−0.158777	−	0.900470i
$915$	20.0031	−	23.5218i	0.661283	−	0.777606i
$916$	2.39061	+	2.00596i	0.0789880	+	0.0662788i
$917$			12.0175i			0.396854i
$918$	0.624136	+	44.2204i	0.0205996	+	1.45949i
$919$	−15.3144			−0.505176			−0.252588	−	0.967574i	$-0.581282\pi$
$919$	−15.3144			−0.505176			−0.252588	+	0.967574i	$0.581282\pi$
$920$	31.4393	−	3.31495i	1.03652	−	0.109291i
$921$	−28.3123	−	14.0526i	−0.932924	−	0.463049i
$922$	−42.0570	+	7.41579i	−1.38507	+	0.244226i
$923$	−1.39045	+	3.82023i	−0.0457673	+	0.125745i
$924$	3.22538	−	4.37527i	0.106107	−	0.143936i
$925$	3.25143	−	23.2471i	0.106906	−	0.764359i
$926$	14.2794	−	24.7327i	0.469252	−	0.812768i
$927$	5.39114	+	4.99125i	0.177068	+	0.163934i
$928$	−31.7427	+	18.3267i	−1.04201	+	0.601603i
$929$	0.281736	−	0.102544i	0.00924347	−	0.00336435i	−0.337394	−	0.941363i	$-0.609546\pi$
$929$	0.281736	−	0.102544i	0.00924347	−	0.00336435i	0.346638	+	0.937999i	$0.387323\pi$
$930$	3.57721	+	6.29142i	0.117301	+	0.206304i
$931$	11.8586	−	9.95056i	0.388651	−	0.326117i
$932$	3.64773	+	4.34720i	0.119485	+	0.142397i
$933$	−7.85990	−	2.31286i	−0.257321	−	0.0757198i
$934$	−19.2045	+	6.98986i	−0.628390	+	0.228715i
$935$	9.80249	−	39.3713i	0.320576	−	1.28758i
$936$	−3.65281	−	0.829512i	−0.119396	−	0.0271135i
$937$	−13.1951	−	7.61820i	−0.431065	−	0.248876i	0.268735	−	0.963214i	$-0.413394\pi$
$937$	−13.1951	−	7.61820i	−0.431065	−	0.248876i	−0.699800	+	0.714338i	$0.746728\pi$
$938$	8.87151	+	1.56429i	0.289665	+	0.0510758i
$939$	−35.6055	+	48.2992i	−1.16194	+	1.57619i
$940$	4.40169	+	9.01721i	0.143567	+	0.294109i
$941$	−1.63828	−	9.29115i	−0.0534064	−	0.302883i	0.946391	−	0.323024i	$-0.104699\pi$
$941$	−1.63828	−	9.29115i	−0.0534064	−	0.302883i	−0.999797	+	0.0201414i	$0.993588\pi$
$942$	−15.0106	+	30.2425i	−0.489072	+	0.985353i
$943$	24.8938	−	29.6673i	0.810654	−	0.966100i
$944$	−66.5014			−2.16444
$945$	12.8647	−	6.50622i	0.418489	−	0.211647i
$946$	−12.5357			−0.407570
$947$	−36.2626	+	43.2160i	−1.17837	+	1.40433i	−0.282941	+	0.959137i	$0.591310\pi$
$947$	−36.2626	+	43.2160i	−1.17837	+	1.40433i	−0.895433	+	0.445195i	$0.853134\pi$
$948$	−1.57605	+	0.0992362i	−0.0511878	+	0.00322304i
$949$	0.146959	+	0.833444i	0.00477048	+	0.0270547i
$950$	−22.2360	−	7.20860i	−0.721430	−	0.233878i
$951$	−0.715159	−	1.63671i	−0.0231906	−	0.0530740i
$952$	13.3176	+	2.34825i	0.431626	+	0.0761073i
$953$	−13.0557	−	7.53769i	−0.422915	−	0.244170i	0.273409	−	0.961898i	$-0.411849\pi$
$953$	−13.0557	−	7.53769i	−0.422915	−	0.244170i	−0.696324	+	0.717728i	$0.745182\pi$
$954$	−36.1275	+	18.5716i	−1.16967	+	0.601278i
$955$	−8.24423	−	2.05261i	−0.266777	−	0.0664210i
$956$	−19.3031	+	7.02574i	−0.624306	+	0.227229i
$957$	13.4873	+	55.7377i	0.435984	+	1.80174i
$958$	24.2012	+	28.8419i	0.781907	+	0.931840i
$959$	14.0671	−	11.8037i	0.454249	−	0.381160i
$960$	0.0875210	−	13.2620i	0.00282473	−	0.428028i
$961$	27.9239	−	10.1635i	0.900770	−	0.327853i
$962$	3.96422	−	2.28875i	0.127812	−	0.0737921i
$963$	−18.9159	−	7.94928i	−0.609557	−	0.256162i
$964$	−4.73403	+	8.19958i	−0.152473	+	0.264091i
$965$	−16.4455	+	11.9567i	−0.529401	+	0.384900i
$966$	−23.5789	−	2.64360i	−0.758638	−	0.0850563i
$967$	−3.00739	+	8.26273i	−0.0967110	+	0.265711i	−0.978609	−	0.205729i	$-0.934043\pi$
$967$	−3.00739	+	8.26273i	−0.0967110	+	0.265711i	0.881898	+	0.471440i	$0.156266\pi$
$968$	−2.82842	+	0.498727i	−0.0909089	+	0.0160297i
$969$	21.1077	−	14.0255i	0.678079	−	0.450563i
$970$	−50.8230	+	5.35877i	−1.63183	+	0.172060i
$971$	−1.79910			−0.0577358			−0.0288679	−	0.999583i	$-0.509190\pi$
$971$	−1.79910			−0.0577358			−0.0288679	+	0.999583i	$0.509190\pi$
$972$	−11.2081	−	0.388579i	−0.359501	−	0.0124637i
$973$		−	3.39195i		−	0.108741i
$974$	4.07041	+	3.41548i	0.130424	+	0.109439i
$975$	−2.98374	−	4.16137i	−0.0955562	−	0.133270i
$976$	6.81303	+	38.6386i	0.218080	+	1.23679i
$977$	−4.35167	+	11.9561i	−0.139222	+	0.382510i	−0.989635	−	0.143606i	$-0.954130\pi$
$977$	−4.35167	+	11.9561i	−0.139222	+	0.382510i	0.850413	+	0.526116i	$0.176352\pi$
$978$	4.28107	−	38.1839i	0.136893	−	1.22099i
$979$	7.97027	−	45.2017i	0.254731	−	1.44465i
$980$	−2.42409	−	8.44324i	−0.0774348	−	0.269709i
$981$	−21.8441	+	51.9798i	−0.697430	+	1.65959i
$982$	−37.3586	+	21.5690i	−1.19216	+	0.688295i
$983$	17.9343	+	49.2740i	0.572015	+	1.57160i	0.801315	+	0.598242i	$0.204134\pi$
$983$	17.9343	+	49.2740i	0.572015	+	1.57160i	−0.229301	+	0.973356i	$0.573644\pi$
$984$	−14.5919	−	15.3214i	−0.465172	−	0.488429i
$985$	−15.0388	−	1.04660i	−0.479176	−	0.0333475i
$986$	61.4007	−	51.5213i	1.95540	−	1.64077i
$987$	3.15266	+	13.0287i	0.100350	+	0.414707i
$988$	−0.412451	−	1.13320i	−0.0131218	−	0.0360519i
$989$	7.23795	+	12.5365i	0.230154	+	0.398638i
$990$	37.2365	+	11.2248i	1.18345	+	0.356748i
$991$	−7.43264	+	12.8737i	−0.236106	+	0.408947i	−0.959593	−	0.281390i	$-0.909204\pi$
$991$	−7.43264	+	12.8737i	−0.236106	+	0.408947i	0.723488	+	0.690337i	$0.242538\pi$
$992$	−4.34332	−	0.765844i	−0.137900	−	0.0243156i
$993$	20.1486	−	8.80392i	0.639397	−	0.279384i
$994$	13.2201	+	4.81172i	0.419316	+	0.152618i
$995$	19.6651	+	13.2548i	0.623424	+	0.420204i
$996$	−0.119690	−	1.90089i	−0.00379252	−	0.0602321i
$997$	−14.5685	+	17.3621i	−0.461390	+	0.549864i	−0.945703	−	0.325031i	$-0.894625\pi$
$997$	−14.5685	+	17.3621i	−0.461390	+	0.549864i	0.484313	+	0.874895i	$0.339070\pi$
$998$			56.4909i			1.78819i
$999$	−18.4639	+	15.9425i	−0.584172	+	0.504397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.4	yes	96
3.2	odd	2		405.2.p.a.289.13		96
5.2	odd	4		675.2.l.h.151.4		96
5.3	odd	4		675.2.l.h.151.13		96
5.4	even	2	inner	135.2.p.a.124.13	yes	96
15.14	odd	2		405.2.p.a.289.4		96
27.5	odd	18		405.2.p.a.199.4		96
27.22	even	9	inner	135.2.p.a.49.13	yes	96
135.22	odd	36		675.2.l.h.76.4		96
135.49	even	18	inner	135.2.p.a.49.4	✓	96
135.59	odd	18		405.2.p.a.199.13		96
135.103	odd	36		675.2.l.h.76.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.4	✓	96	135.49	even	18	inner
135.2.p.a.49.13	yes	96	27.22	even	9	inner
135.2.p.a.124.4	yes	96	1.1	even	1	trivial
135.2.p.a.124.13	yes	96	5.4	even	2	inner
405.2.p.a.199.4		96	27.5	odd	18
405.2.p.a.199.13		96	135.59	odd	18
405.2.p.a.289.4		96	15.14	odd	2
405.2.p.a.289.13		96	3.2	odd	2
675.2.l.h.76.4		96	135.22	odd	36
675.2.l.h.76.13		96	135.103	odd	36
675.2.l.h.151.4		96	5.2	odd	4
675.2.l.h.151.13		96	5.3	odd	4

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06000 + 1.26326i) q^{2} +(0.958575 + 1.44261i) q^{3} +(-0.124928 - 0.708504i) q^{4} +(-2.00944 + 0.980894i) q^{5} +(-2.83849 - 0.318243i) q^{6} +(1.22191 + 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +(-1.16227 + 2.76571i) q^{9} +O(q^{10})\)	\(q+(-1.06000 + 1.26326i) q^{2} +(0.958575 + 1.44261i) q^{3} +(-0.124928 - 0.708504i) q^{4} +(-2.00944 + 0.980894i) q^{5} +(-2.83849 - 0.318243i) q^{6} +(1.22191 + 0.215456i) q^{7} +(-1.82882 - 1.05587i) q^{8} +(-1.16227 + 2.76571i) q^{9} +(0.890884 - 3.57820i) q^{10} +(3.30366 - 1.20243i) q^{11} +(0.902344 - 0.859377i) q^{12} +(-0.380059 - 0.452936i) q^{13} +(-1.56741 + 1.31521i) q^{14} +(-3.34125 - 1.95858i) q^{15} +(4.62449 - 1.68318i) q^{16} +(-4.46967 + 2.58056i) q^{17} +(-2.26180 - 4.39990i) q^{18} +(-1.41748 + 2.45515i) q^{19} +(0.946003 + 1.30115i) q^{20} +(0.860474 + 1.96928i) q^{21} +(-1.98290 + 5.44797i) q^{22} +(6.59324 - 1.16257i) q^{23} +(-0.229849 - 3.65042i) q^{24} +(3.07569 - 3.94210i) q^{25} +0.975040 q^{26} +(-5.10397 + 0.974431i) q^{27} -0.892646i q^{28} +(7.21421 + 6.05345i) q^{29} +(6.01593 - 2.14477i) q^{30} +(0.196771 + 1.11595i) q^{31} +(-1.33116 + 3.65733i) q^{32} +(4.90146 + 3.61329i) q^{33} +(1.47793 - 8.38176i) q^{34} +(-2.66670 + 0.765621i) q^{35} +(2.10471 + 0.477957i) q^{36} +(4.06570 - 2.34734i) q^{37} +(-1.59896 - 4.39311i) q^{38} +(0.289098 - 0.982452i) q^{39} +(4.71061 + 0.327827i) q^{40} +(4.43129 - 3.71830i) q^{41} +(-3.39982 - 1.00044i) q^{42} +(0.739520 + 2.03181i) q^{43} +(-1.26465 - 2.19044i) q^{44} +(-0.377357 - 6.69758i) q^{45} +(-5.52022 + 9.56131i) q^{46} +(6.14268 + 1.08312i) q^{47} +(6.86110 + 5.05791i) q^{48} +(-5.13120 - 1.86760i) q^{49} +(1.71966 + 8.06403i) q^{50} +(-8.00727 - 3.97434i) q^{51} +(-0.273427 + 0.325858i) q^{52} -8.21098i q^{53} +(4.17926 - 7.48054i) q^{54} +(-5.45905 + 5.65676i) q^{55} +(-2.00717 - 1.68421i) q^{56} +(-4.90059 + 0.308566i) q^{57} +(-15.2942 + 2.69677i) q^{58} +(-12.6981 - 4.62173i) q^{59} +(-0.970247 + 2.61197i) q^{60} +(-1.38440 + 7.85133i) q^{61} +(-1.61831 - 0.934331i) q^{62} +(-2.01608 + 3.12903i) q^{63} +(1.71215 + 2.96553i) q^{64} +(1.20799 + 0.537351i) q^{65} +(-9.76008 + 2.36173i) q^{66} +(-2.83000 - 3.37266i) q^{67} +(2.38673 + 2.84439i) q^{68} +(7.99725 + 8.39709i) q^{69} +(1.85953 - 4.18030i) q^{70} +(-3.43788 - 5.95458i) q^{71} +(5.04582 - 3.83078i) q^{72} +(-1.23957 - 0.715668i) q^{73} +(-1.34436 + 7.62423i) q^{74} +(8.63520 + 0.658243i) q^{75} +(1.91656 + 0.697573i) q^{76} +(4.29586 - 0.757476i) q^{77} +(0.934649 + 1.40661i) q^{78} +(-0.970806 - 0.814603i) q^{79} +(-7.64162 + 7.91838i) q^{80} +(-6.29826 - 6.42899i) q^{81} +9.53928i q^{82} +(0.982501 - 1.17090i) q^{83} +(1.28774 - 0.855668i) q^{84} +(6.45027 - 9.56976i) q^{85} +(-3.35061 - 1.21952i) q^{86} +(-1.81742 + 16.2100i) q^{87} +(-7.31144 - 1.28920i) q^{88} +(6.52774 - 11.3064i) q^{89} +(8.86079 + 6.62275i) q^{90} +(-0.366811 - 0.635335i) q^{91} +(-1.64736 - 4.52610i) q^{92} +(-1.42126 + 1.35358i) q^{93} +(-7.87952 + 6.61170i) q^{94} +(0.440100 - 6.32387i) q^{95} +(-6.55214 + 1.58548i) q^{96} +(-4.74011 - 13.0234i) q^{97} +(7.79835 - 4.50238i) q^{98} +(-0.514163 + 10.5345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

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