LMFDB - Embedded newform 288.2.v.d.109.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.5
Character	$\chi$	$=$	288.109
Dual form			288.2.v.d.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.333592 + 1.37431i) q^{2} +(-1.77743 - 0.916914i) q^{4} +(1.20409 - 0.498752i) q^{5} +(2.59422 - 2.59422i) q^{7} +(1.85306 - 2.13686i) q^{8} +O(q^{10})$	\(q+(-0.333592 + 1.37431i) q^{2} +(-1.77743 - 0.916914i) q^{4} +(1.20409 - 0.498752i) q^{5} +(2.59422 - 2.59422i) q^{7} +(1.85306 - 2.13686i) q^{8} +(0.283762 + 1.82117i) q^{10} +(-2.14608 - 5.18109i) q^{11} +(-0.984096 - 0.407626i) q^{13} +(2.69984 + 4.43066i) q^{14} +(2.31854 + 3.25951i) q^{16} +0.979053i q^{17} +(5.68961 + 2.35671i) q^{19} +(-2.59751 - 0.217551i) q^{20} +(7.83631 - 1.22100i) q^{22} +(3.70206 + 3.70206i) q^{23} +(-2.33445 + 2.33445i) q^{25} +(0.888489 - 1.21647i) q^{26} +(-6.98973 + 2.23238i) q^{28} +(1.17302 - 2.83193i) q^{29} +1.54469 q^{31} +(-5.25300 + 2.09904i) q^{32} +(-1.34552 - 0.326604i) q^{34} +(1.82981 - 4.41756i) q^{35} +(-8.23352 + 3.41044i) q^{37} +(-5.13685 + 7.03308i) q^{38} +(1.16549 - 3.49720i) q^{40} +(1.10862 + 1.10862i) q^{41} +(-3.47106 - 8.37989i) q^{43} +(-0.936101 + 11.1768i) q^{44} +(-6.32273 + 3.85278i) q^{46} -3.15582i q^{47} -6.45997i q^{49} +(-2.42949 - 3.98700i) q^{50} +(1.37541 + 1.62686i) q^{52} +(2.55252 + 6.16232i) q^{53} +(-5.16815 - 5.16815i) q^{55} +(-0.736256 - 10.3507i) q^{56} +(3.50063 + 2.55680i) q^{58} +(8.95423 - 3.70896i) q^{59} +(-2.00717 + 4.84573i) q^{61} +(-0.515295 + 2.12287i) q^{62} +(-1.13236 - 7.91945i) q^{64} -1.38825 q^{65} +(1.14380 - 2.76138i) q^{67} +(0.897707 - 1.74020i) q^{68} +(5.46066 + 3.98838i) q^{70} +(-10.0373 + 10.0373i) q^{71} +(8.11103 + 8.11103i) q^{73} +(-1.94035 - 12.4531i) q^{74} +(-7.95200 - 9.40578i) q^{76} +(-19.0083 - 7.87349i) q^{77} +0.155459i q^{79} +(4.41742 + 2.76837i) q^{80} +(-1.89342 + 1.15376i) q^{82} +(-5.13862 - 2.12849i) q^{83} +(0.488304 + 1.17887i) q^{85} +(12.6745 - 1.97484i) q^{86} +(-15.0481 - 5.01498i) q^{88} +(6.15303 - 6.15303i) q^{89} +(-3.61044 + 1.49549i) q^{91} +(-3.18569 - 9.97462i) q^{92} +(4.33707 + 1.05276i) q^{94} +8.02623 q^{95} +14.3852 q^{97} +(8.87798 + 2.15499i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.333592	+	1.37431i	−0.235885	+	0.971781i
$2$	−0.333592	+	1.37431i	−0.235885	+	0.971781i
$3$		0			0
$3$		0			0
$4$	−1.77743	−	0.916914i	−0.888717	−	0.458457i
$5$	1.20409	−	0.498752i	0.538487	−	0.223048i	−0.0968290	−	0.995301i	$-0.530870\pi$
$5$	1.20409	−	0.498752i	0.538487	−	0.223048i	0.635316	+	0.772253i	$0.280870\pi$
$6$		0			0
$7$	2.59422	−	2.59422i	0.980524	−	0.980524i	−0.0192902	−	0.999814i	$-0.506141\pi$
$7$	2.59422	−	2.59422i	0.980524	−	0.980524i	0.999814	+	0.0192902i	$0.00614065\pi$
$8$	1.85306	−	2.13686i	0.655154	−	0.755495i
$9$		0			0
$10$	0.283762	+	1.82117i	0.0897334	+	0.575905i
$11$	−2.14608	−	5.18109i	−0.647066	−	1.56216i	−0.816960	−	0.576694i	$-0.804342\pi$
$11$	−2.14608	−	5.18109i	−0.647066	−	1.56216i	0.169894	−	0.985462i	$-0.445658\pi$
$12$		0			0
$13$	−0.984096	−	0.407626i	−0.272939	−	0.113055i	0.242016	−	0.970272i	$-0.422191\pi$
$13$	−0.984096	−	0.407626i	−0.272939	−	0.113055i	−0.514955	+	0.857217i	$0.672191\pi$
$14$	2.69984	+	4.43066i	0.721564	+	1.18414i
$15$		0			0
$16$	2.31854	+	3.25951i	0.579635	+	0.814876i
$17$			0.979053i			0.237455i	0.992927	+	0.118728i	$0.0378815\pi$
$17$			0.979053i			0.237455i	−0.992927	+	0.118728i	$0.962118\pi$
$18$		0			0
$19$	5.68961	+	2.35671i	1.30529	+	0.540667i	0.923505	−	0.383586i	$-0.125311\pi$
$19$	5.68961	+	2.35671i	1.30529	+	0.540667i	0.381781	+	0.924253i	$0.375311\pi$
$20$	−2.59751	−	0.217551i	−0.580820	−	0.0486459i
$21$		0			0
$22$	7.83631	−	1.22100i	1.67071	−	0.260318i
$23$	3.70206	+	3.70206i	0.771932	+	0.771932i	0.978444	−	0.206512i	$-0.0662113\pi$
$23$	3.70206	+	3.70206i	0.771932	+	0.771932i	−0.206512	+	0.978444i	$0.566211\pi$
$24$		0			0
$25$	−2.33445	+	2.33445i	−0.466890	+	0.466890i
$26$	0.888489	−	1.21647i	0.174247	−	0.238569i
$27$		0			0
$28$	−6.98973	+	2.23238i	−1.32094	+	0.421880i
$29$	1.17302	−	2.83193i	0.217825	−	0.525876i	−0.776761	−	0.629796i	$-0.783139\pi$
$29$	1.17302	−	2.83193i	0.217825	−	0.525876i	0.994586	+	0.103920i	$0.0331385\pi$
$30$		0			0
$31$	1.54469			0.277434			0.138717	−	0.990332i	$-0.455702\pi$
$31$	1.54469			0.277434			0.138717	+	0.990332i	$0.455702\pi$
$32$	−5.25300	+	2.09904i	−0.928608	+	0.371061i
$33$		0			0
$34$	−1.34552	−	0.326604i	−0.230755	−	0.0560121i
$35$	1.82981	−	4.41756i	0.309295	−	0.746703i
$36$		0			0
$37$	−8.23352	+	3.41044i	−1.35358	+	0.560672i	−0.937288	−	0.348557i	$-0.886672\pi$
$37$	−8.23352	+	3.41044i	−1.35358	+	0.560672i	−0.416295	+	0.909229i	$0.636672\pi$
$38$	−5.13685	+	7.03308i	−0.833307	+	1.14092i
$39$		0			0
$40$	1.16549	−	3.49720i	0.184280	−	0.552955i
$41$	1.10862	+	1.10862i	0.173138	+	0.173138i	0.788357	−	0.615219i	$-0.210932\pi$
$41$	1.10862	+	1.10862i	0.173138	+	0.173138i	−0.615219	+	0.788357i	$0.710932\pi$
$42$		0			0
$43$	−3.47106	−	8.37989i	−0.529332	−	1.27792i	−0.931961	−	0.362558i	$-0.881903\pi$
$43$	−3.47106	−	8.37989i	−0.529332	−	1.27792i	0.402629	−	0.915363i	$-0.368097\pi$
$44$	−0.936101	+	11.1768i	−0.141123	+	1.68497i
$45$		0			0
$46$	−6.32273	+	3.85278i	−0.932236	+	0.568062i
$47$		−	3.15582i		−	0.460324i	−0.973152	−	0.230162i	$-0.926074\pi$
$47$		−	3.15582i		−	0.460324i	0.973152	−	0.230162i	$-0.0739256\pi$
$48$		0			0
$49$		−	6.45997i		−	0.922853i
$50$	−2.42949	−	3.98700i	−0.343582	−	0.563847i
$51$		0			0
$52$	1.37541	+	1.62686i	0.190735	+	0.225605i
$53$	2.55252	+	6.16232i	0.350615	+	0.846460i	0.996544	+	0.0830627i	$0.0264702\pi$
$53$	2.55252	+	6.16232i	0.350615	+	0.846460i	−0.645929	+	0.763397i	$0.723530\pi$
$54$		0			0
$55$	−5.16815	−	5.16815i	−0.696873	−	0.696873i
$56$	−0.736256	−	10.3507i	−0.0983864	−	1.38318i
$57$		0			0
$58$	3.50063	+	2.55680i	0.459655	+	0.335724i
$59$	8.95423	−	3.70896i	1.16574	−	0.482866i	0.285958	−	0.958242i	$-0.407688\pi$
$59$	8.95423	−	3.70896i	1.16574	−	0.482866i	0.879783	+	0.475376i	$0.157688\pi$
$60$		0			0
$61$	−2.00717	+	4.84573i	−0.256991	+	0.620432i	−0.998737	−	0.0502499i	$-0.983998\pi$
$61$	−2.00717	+	4.84573i	−0.256991	+	0.620432i	0.741746	+	0.670681i	$0.233998\pi$
$62$	−0.515295	+	2.12287i	−0.0654425	+	0.269605i
$63$		0			0
$64$	−1.13236	−	7.91945i	−0.141545	−	0.989932i
$65$	−1.38825			−0.172191
$66$		0			0
$67$	1.14380	−	2.76138i	0.139738	−	0.337357i	−0.838482	−	0.544930i	$-0.816556\pi$
$67$	1.14380	−	2.76138i	0.139738	−	0.337357i	0.978220	+	0.207573i	$0.0665564\pi$
$68$	0.897707	−	1.74020i	0.108863	−	0.211030i
$69$		0			0
$70$	5.46066	+	3.98838i	0.652674	+	0.476703i
$71$	−10.0373	+	10.0373i	−1.19120	+	1.19120i	−0.214474	+	0.976730i	$0.568804\pi$
$71$	−10.0373	+	10.0373i	−1.19120	+	1.19120i	−0.976730	+	0.214474i	$0.931196\pi$
$72$		0			0
$73$	8.11103	+	8.11103i	0.949324	+	0.949324i	0.998776	−	0.0494525i	$-0.0157476\pi$
$73$	8.11103	+	8.11103i	0.949324	+	0.949324i	−0.0494525	+	0.998776i	$0.515748\pi$
$74$	−1.94035	−	12.4531i	−0.225561	−	1.44764i
$75$		0			0
$76$	−7.95200	−	9.40578i	−0.912157	−	1.07892i
$77$	−19.0083	−	7.87349i	−2.16620	−	0.897268i
$78$		0			0
$79$			0.155459i			0.0174905i	0.999962	+	0.00874523i	$0.00278373\pi$
$79$			0.155459i			0.0174905i	−0.999962	+	0.00874523i	$0.997216\pi$
$80$	4.41742	+	2.76837i	0.493883	+	0.309513i
$81$		0			0
$82$	−1.89342	+	1.15376i	−0.209093	+	0.127412i
$83$	−5.13862	−	2.12849i	−0.564037	−	0.233632i	0.0823997	−	0.996599i	$-0.473742\pi$
$83$	−5.13862	−	2.12849i	−0.564037	−	0.233632i	−0.646437	+	0.762968i	$0.723742\pi$
$84$		0			0
$85$	0.488304	+	1.17887i	0.0529640	+	0.127866i
$86$	12.6745	−	1.97484i	1.36672	−	0.212953i
$87$		0			0
$88$	−15.0481	−	5.01498i	−1.60413	−	0.534598i
$89$	6.15303	−	6.15303i	0.652220	−	0.652220i	−0.301307	−	0.953527i	$-0.597423\pi$
$89$	6.15303	−	6.15303i	0.652220	−	0.652220i	0.953527	+	0.301307i	$0.0974230\pi$
$90$		0			0
$91$	−3.61044	+	1.49549i	−0.378477	+	0.156770i
$92$	−3.18569	−	9.97462i	−0.332131	−	1.03993i
$93$		0			0
$94$	4.33707	+	1.05276i	0.447334	+	0.108583i
$95$	8.02623			0.823474
$96$		0			0
$97$	14.3852			1.46059			0.730296	−	0.683131i	$-0.239382\pi$
$97$	14.3852			1.46059			0.730296	+	0.683131i	$0.239382\pi$
$98$	8.87798	+	2.15499i	0.896811	+	0.217687i
$99$		0			0
$100$	6.28981	−	2.00884i	0.628981	−	0.200884i
$101$	−12.1198	+	5.02020i	−1.20597	+	0.499528i	−0.892923	−	0.450210i	$-0.851349\pi$
$101$	−12.1198	+	5.02020i	−1.20597	+	0.499528i	−0.313045	+	0.949738i	$0.601349\pi$
$102$		0			0
$103$	−10.3057	+	10.3057i	−1.01545	+	1.01545i	−0.0155752	+	0.999879i	$0.504958\pi$
$103$	−10.3057	+	10.3057i	−1.01545	+	1.01545i	−0.999879	+	0.0155752i	$0.995042\pi$
$104$	−2.69463	+	1.34752i	−0.264230	+	0.132136i
$105$		0			0
$106$	−9.32041	+	1.45224i	−0.905279	+	0.141054i
$107$	0.576841	+	1.39262i	0.0557653	+	0.134629i	0.949307	−	0.314352i	$-0.101787\pi$
$107$	0.576841	+	1.39262i	0.0557653	+	0.134629i	−0.893541	+	0.448981i	$0.851787\pi$
$108$		0			0
$109$	−11.0738	−	4.58693i	−1.06068	−	0.439348i	−0.216987	−	0.976174i	$-0.569623\pi$
$109$	−11.0738	−	4.58693i	−1.06068	−	0.439348i	−0.843693	+	0.536826i	$0.819623\pi$
$110$	8.82667	−	5.37857i	0.841590	−	0.512826i
$111$		0			0
$112$	14.4707	+	2.44108i	1.36735	+	0.230660i
$113$			9.41139i			0.885349i	0.896682	+	0.442675i	$0.145970\pi$
$113$			9.41139i			0.885349i	−0.896682	+	0.442675i	$0.854030\pi$
$114$		0			0
$115$	6.30402	+	2.61121i	0.587853	+	0.243497i
$116$	−4.68161	+	3.95801i	−0.434676	+	0.367492i
$117$		0			0
$118$	2.11019	+	13.5431i	0.194259	+	1.24675i
$119$	2.53988	+	2.53988i	0.232831	+	0.232831i
$120$		0			0
$121$	−14.4598	+	14.4598i	−1.31453	+	1.31453i
$122$	−5.98994	−	4.37495i	−0.542303	−	0.396090i
$123$		0			0
$124$	−2.74558	−	1.41635i	−0.246560	−	0.127192i
$125$	−4.14034	+	9.99566i	−0.370323	+	0.894039i
$126$		0			0
$127$	16.0219			1.42171			0.710855	−	0.703338i	$-0.248308\pi$
$127$	16.0219			1.42171			0.710855	+	0.703338i	$0.248308\pi$
$128$	11.2615	+	1.08565i	0.995385	+	0.0959586i
$129$		0			0
$130$	0.463107	−	1.90788i	0.0406172	−	0.167332i
$131$	−2.18619	+	5.27794i	−0.191009	+	0.461135i	−0.990151	−	0.140007i	$-0.955288\pi$
$131$	−2.18619	+	5.27794i	−0.191009	+	0.461135i	0.799142	+	0.601142i	$0.205288\pi$
$132$		0			0
$133$	20.8739	−	8.64627i	1.81000	−	0.749727i
$134$	3.41342	+	2.49311i	0.294875	+	0.215372i
$135$		0			0
$136$	2.09210	+	1.81424i	0.179396	+	0.155570i
$137$	8.63573	+	8.63573i	0.737801	+	0.737801i	0.972152	−	0.234351i	$-0.0752966\pi$
$137$	8.63573	+	8.63573i	0.737801	+	0.737801i	−0.234351	+	0.972152i	$0.575297\pi$
$138$		0			0
$139$	−4.05369	−	9.78647i	−0.343829	−	0.830078i	−0.997321	−	0.0731441i	$-0.976697\pi$
$139$	−4.05369	−	9.78647i	−0.343829	−	0.830078i	0.653492	−	0.756933i	$-0.273303\pi$
$140$	−7.30288	+	6.17413i	−0.617206	+	0.521809i
$141$		0			0
$142$	−10.4459	−	17.1426i	−0.876602	−	1.43858i
$143$			5.97348i			0.499528i
$144$		0			0
$145$		−	3.99495i		−	0.331763i
$146$	−13.8528	+	8.44126i	−1.14647	+	0.698604i
$147$		0			0
$148$	17.7616	+	1.48760i	1.46000	+	0.122280i
$149$	−1.10547	−	2.66884i	−0.0905637	−	0.218640i	0.872107	−	0.489315i	$-0.162753\pi$
$149$	−1.10547	−	2.66884i	−0.0905637	−	0.218640i	−0.962671	+	0.270675i	$0.912753\pi$
$150$		0			0
$151$	6.40487	+	6.40487i	0.521221	+	0.521221i	0.917940	−	0.396719i	$-0.129851\pi$
$151$	6.40487	+	6.40487i	0.521221	+	0.521221i	−0.396719	+	0.917940i	$0.629851\pi$
$152$	15.5791	−	7.79079i	1.26363	−	0.631916i
$153$		0			0
$154$	17.1616	−	23.4967i	1.38292	−	1.89342i
$155$	1.85995	−	0.770416i	0.149395	−	0.0618813i
$156$		0			0
$157$	−2.85724	+	6.89798i	−0.228032	+	0.550519i	−0.995938	−	0.0900446i	$-0.971299\pi$
$157$	−2.85724	+	6.89798i	−0.228032	+	0.550519i	0.767905	+	0.640563i	$0.221299\pi$
$158$	−0.213648	−	0.0518597i	−0.0169969	−	0.00412573i
$159$		0			0
$160$	−5.27820	+	5.14738i	−0.417279	+	0.406936i
$161$	19.2079			1.51379
$162$		0			0
$163$	0.958379	−	2.31373i	0.0750661	−	0.181225i	−0.881892	−	0.471451i	$-0.843730\pi$
$163$	0.958379	−	2.31373i	0.0750661	−	0.181225i	0.956958	+	0.290226i	$0.0937304\pi$
$164$	−0.953993	−	2.98702i	−0.0744943	−	0.233247i
$165$		0			0
$166$	4.63939	−	6.35199i	0.360087	−	0.493010i
$167$	−3.60896	+	3.60896i	−0.279270	+	0.279270i	−0.832817	−	0.553548i	$-0.813274\pi$
$167$	−3.60896	+	3.60896i	−0.279270	+	0.279270i	0.553548	+	0.832817i	$0.313274\pi$
$168$		0			0
$169$	−8.39010	−	8.39010i	−0.645392	−	0.645392i
$170$	−1.78302	+	0.277818i	−0.136752	+	0.0213077i
$171$		0			0
$172$	−1.51405	+	18.0774i	−0.115445	+	1.37839i
$173$	2.16959	+	0.898673i	0.164951	+	0.0683248i	0.463631	−	0.886028i	$-0.346546\pi$
$173$	2.16959	+	0.898673i	0.164951	+	0.0683248i	−0.298680	+	0.954353i	$0.596546\pi$
$174$		0			0
$175$			12.1122i			0.915593i
$176$	11.9120	−	19.0077i	0.897902	−	1.43276i
$177$		0			0
$178$	6.40354	+	10.5087i	0.479966	+	0.787663i
$179$	2.66481	+	1.10380i	0.199177	+	0.0825020i	0.480042	−	0.877245i	$-0.340621\pi$
$179$	2.66481	+	1.10380i	0.199177	+	0.0825020i	−0.280865	+	0.959747i	$0.590621\pi$
$180$		0			0
$181$	−1.10884	−	2.67697i	−0.0824191	−	0.198977i	0.877298	−	0.479947i	$-0.159344\pi$
$181$	−1.10884	−	2.67697i	−0.0824191	−	0.198977i	−0.959717	+	0.280969i	$0.909344\pi$
$182$	−0.850852	−	5.46073i	−0.0630693	−	0.404776i
$183$		0			0
$184$	14.7709	−	1.05067i	1.08893	−	0.0774562i
$185$	−8.21296	+	8.21296i	−0.603829	+	0.603829i
$186$		0			0
$187$	5.07256	−	2.10112i	0.370942	−	0.153649i
$188$	−2.89362	+	5.60927i	−0.211039	+	0.409098i
$189$		0			0
$190$	−2.67748	+	11.0305i	−0.194245	+	0.800236i
$191$	−8.35300			−0.604402			−0.302201	−	0.953244i	$-0.597721\pi$
$191$	−8.35300			−0.604402			−0.302201	+	0.953244i	$0.597721\pi$
$192$		0			0
$193$	−12.3350			−0.887894			−0.443947	−	0.896053i	$-0.646422\pi$
$193$	−12.3350			−0.887894			−0.443947	+	0.896053i	$0.646422\pi$
$194$	−4.79877	+	19.7696i	−0.344532	+	1.41938i
$195$		0			0
$196$	−5.92324	+	11.4822i	−0.423088	+	0.820155i
$197$	21.5154	−	8.91197i	1.53291	−	0.634952i	0.552782	−	0.833326i	$-0.313566\pi$
$197$	21.5154	−	8.91197i	1.53291	−	0.634952i	0.980126	+	0.198374i	$0.0635661\pi$
$198$		0			0
$199$	−17.0334	+	17.0334i	−1.20746	+	1.20746i	−0.235616	+	0.971846i	$0.575711\pi$
$199$	−17.0334	+	17.0334i	−1.20746	+	1.20746i	−0.971846	+	0.235616i	$0.924289\pi$
$200$	0.662531	+	9.31426i	0.0468480	+	0.658617i
$201$		0			0
$202$	−2.85622	−	18.3310i	−0.200963	−	1.28977i
$203$	−4.30357	−	10.3897i	−0.302051	−	0.729217i
$204$		0			0
$205$	1.88781	+	0.781958i	0.131851	+	0.0546143i
$206$	−10.7253	−	17.6011i	−0.747269	−	1.22633i
$207$		0			0
$208$	−0.953006	−	4.15276i	−0.0660791	−	0.287942i
$209$		−	34.5360i		−	2.38891i
$210$		0			0
$211$	−8.86549	−	3.67221i	−0.610325	−	0.252805i	0.0560422	−	0.998428i	$-0.482152\pi$
$211$	−8.86549	−	3.67221i	−0.610325	−	0.252805i	−0.666368	+	0.745623i	$0.732152\pi$
$212$	1.11339	−	13.2936i	0.0764677	−	0.913005i
$213$		0			0
$214$	−2.10631	+	0.328191i	−0.143984	+	0.0224347i
$215$	−8.35897	−	8.35897i	−0.570077	−	0.570077i
$216$		0			0
$217$	4.00726	−	4.00726i	0.272031	−	0.272031i
$218$	9.99798	−	13.6887i	0.677149	−	0.927113i
$219$		0			0
$220$	4.44730	+	13.9248i	0.299837	+	0.938809i
$221$	0.399087	−	0.963482i	0.0268455	−	0.0648108i
$222$		0			0
$223$	6.90976			0.462712			0.231356	−	0.972869i	$-0.425684\pi$
$223$	6.90976			0.462712			0.231356	+	0.972869i	$0.425684\pi$
$224$	−8.18208	+	19.0728i	−0.546688	+	1.27436i
$225$		0			0
$226$	−12.9341	−	3.13956i	−0.860365	−	0.208840i
$227$	−1.65113	+	3.98617i	−0.109589	+	0.264572i	−0.969154	−	0.246454i	$-0.920734\pi$
$227$	−1.65113	+	3.98617i	−0.109589	+	0.264572i	0.859565	+	0.511026i	$0.170734\pi$
$228$		0			0
$229$	7.09073	−	2.93708i	0.468568	−	0.194087i	−0.135890	−	0.990724i	$-0.543389\pi$
$229$	7.09073	−	2.93708i	0.468568	−	0.194087i	0.604459	+	0.796636i	$0.293389\pi$
$230$	−5.69157	+	7.79258i	−0.375291	+	0.513827i
$231$		0			0
$232$	−3.87777	−	7.75432i	−0.254588	−	0.509096i
$233$	1.49412	+	1.49412i	0.0978831	+	0.0978831i	0.754353	−	0.656470i	$-0.227951\pi$
$233$	1.49412	+	1.49412i	0.0978831	+	0.0978831i	−0.656470	+	0.754353i	$0.727951\pi$
$234$		0			0
$235$	−1.57397	−	3.79990i	−0.102675	−	0.247878i
$236$	−19.3163	−	1.61782i	−1.25739	−	0.105311i
$237$		0			0
$238$	−4.33786	+	2.64329i	−0.281181	+	0.171339i
$239$			5.41212i			0.350081i	0.984561	+	0.175041i	$0.0560057\pi$
$239$			5.41212i			0.350081i	−0.984561	+	0.175041i	$0.943994\pi$
$240$		0			0
$241$		−	19.6684i		−	1.26695i	−0.773762	−	0.633476i	$-0.781628\pi$
$241$		−	19.6684i		−	1.26695i	0.773762	−	0.633476i	$-0.218372\pi$
$242$	−15.0486	−	24.6959i	−0.967359	−	1.58752i
$243$		0			0
$244$	8.01071	−	6.77256i	0.512833	−	0.433569i
$245$	−3.22192	−	7.77841i	−0.205841	−	0.496944i
$246$		0			0
$247$	−4.63846	−	4.63846i	−0.295138	−	0.295138i
$248$	2.86239	−	3.30079i	0.181762	−	0.209600i
$249$		0			0
$250$	−12.3559	−	9.02456i	−0.781457	−	0.570763i
$251$	−23.6647	+	9.80223i	−1.49370	+	0.618711i	−0.972119	−	0.234490i	$-0.924658\pi$
$251$	−23.6647	+	9.80223i	−1.49370	+	0.618711i	−0.521582	+	0.853201i	$0.674658\pi$
$252$		0			0
$253$	11.2358	−	27.1256i	0.706387	−	1.70537i
$254$	−5.34476	+	22.0189i	−0.335360	+	1.38159i
$255$		0			0
$256$	−5.24875	+	15.1146i	−0.328047	+	0.944661i
$257$	9.44245			0.589004			0.294502	−	0.955651i	$-0.404846\pi$
$257$	9.44245			0.589004			0.294502	+	0.955651i	$0.404846\pi$
$258$		0			0
$259$	−12.5122	+	30.2070i	−0.777468	+	1.87697i
$260$	2.46752	+	1.27290i	0.153029	+	0.0789421i
$261$		0			0
$262$	−6.52420	−	4.76517i	−0.403067	−	0.294393i
$263$	8.38788	−	8.38788i	0.517219	−	0.517219i	−0.399510	−	0.916729i	$-0.630820\pi$
$263$	8.38788	−	8.38788i	0.517219	−	0.517219i	0.916729	+	0.399510i	$0.130820\pi$
$264$		0			0
$265$	6.14694	+	6.14694i	0.377603	+	0.377603i
$266$	4.91925	+	31.5715i	0.301619	+	1.93577i
$267$		0			0
$268$	−4.56498	+	3.85941i	−0.278851	+	0.235751i
$269$	−0.0655084	−	0.0271345i	−0.00399412	−	0.00165442i	0.380685	−	0.924705i	$-0.375688\pi$
$269$	−0.0655084	−	0.0271345i	−0.00399412	−	0.00165442i	−0.384680	+	0.923050i	$0.625688\pi$
$270$		0			0
$271$		−	14.4877i		−	0.880062i	−0.897982	−	0.440031i	$-0.854967\pi$
$271$		−	14.4877i		−	0.880062i	0.897982	−	0.440031i	$-0.145033\pi$
$272$	−3.19123	+	2.26997i	−0.193497	+	0.137637i
$273$		0			0
$274$	−14.7489	+	8.98733i	−0.891017	+	0.542945i
$275$	17.1049	+	7.08507i	1.03146	+	0.427246i
$276$		0			0
$277$	8.16981	+	19.7237i	0.490876	+	1.18508i	0.954275	+	0.298931i	$0.0966299\pi$
$277$	8.16981	+	19.7237i	0.490876	+	1.18508i	−0.463398	+	0.886150i	$0.653370\pi$
$278$	14.8019	−	2.30632i	0.887758	−	0.138324i
$279$		0			0
$280$	−6.04897	−	12.0960i	−0.361495	−	0.722876i
$281$	−2.76272	+	2.76272i	−0.164810	+	0.164810i	−0.784694	−	0.619884i	$-0.787180\pi$
$281$	−2.76272	+	2.76272i	−0.164810	+	0.164810i	0.619884	+	0.784694i	$0.287180\pi$
$282$		0			0
$283$	−5.86879	+	2.43093i	−0.348864	+	0.144504i	−0.550233	−	0.835011i	$-0.685461\pi$
$283$	−5.86879	+	2.43093i	−0.348864	+	0.144504i	0.201369	+	0.979515i	$0.435461\pi$
$284$	27.0439	−	8.63726i	1.60476	−	0.512527i
$285$		0			0
$286$	−8.20940	−	1.99270i	−0.485432	−	0.117831i
$287$	5.75203			0.339532
$288$		0			0
$289$	16.0415			0.943615
$290$	5.49029	+	1.33268i	0.322401	+	0.0782578i
$291$		0			0
$292$	−6.97970	−	21.8539i	−0.408456	−	1.27890i
$293$	−4.51526	+	1.87028i	−0.263784	+	0.109263i	−0.510656	−	0.859785i	$-0.670597\pi$
$293$	−4.51526	+	1.87028i	−0.263784	+	0.109263i	0.246872	+	0.969048i	$0.420597\pi$
$294$		0			0
$295$	8.93187	−	8.93187i	0.520034	−	0.520034i
$296$	−7.96955	+	23.9136i	−0.463221	+	1.38995i
$297$		0			0
$298$	4.03658	−	0.628952i	0.233833	−	0.0364342i
$299$	−2.13412	−	5.15223i	−0.123420	−	0.297961i
$300$		0			0
$301$	−30.7440	−	12.7346i	−1.77206	−	0.734009i
$302$	−10.9389	+	6.66564i	−0.629461	+	0.383564i
$303$		0			0
$304$	5.50986	+	24.0094i	0.316012	+	1.37704i
$305$			6.83578i			0.391416i
$306$		0			0
$307$	8.44200	+	3.49679i	0.481810	+	0.199572i	0.610350	−	0.792132i	$-0.291029\pi$
$307$	8.44200	+	3.49679i	0.481810	+	0.199572i	−0.128539	+	0.991704i	$0.541029\pi$
$308$	26.5667	+	31.4236i	1.51378	+	1.79052i
$309$		0			0
$310$	0.438324	+	2.81314i	0.0248951	+	0.159776i
$311$	−20.8439	−	20.8439i	−1.18195	−	1.18195i	−0.979239	−	0.202710i	$-0.935025\pi$
$311$	−20.8439	−	20.8439i	−1.18195	−	1.18195i	−0.202710	−	0.979239i	$-0.564975\pi$
$312$		0			0
$313$	14.1026	−	14.1026i	0.797124	−	0.797124i	−0.185517	−	0.982641i	$-0.559396\pi$
$313$	14.1026	−	14.1026i	0.797124	−	0.797124i	0.982641	+	0.185517i	$0.0593959\pi$
$314$	−8.52678	−	6.22782i	−0.481194	−	0.351456i
$315$		0			0
$316$	0.142542	−	0.276317i	0.00801862	−	0.0155441i
$317$	−1.07307	+	2.59063i	−0.0602698	+	0.145504i	−0.951145	−	0.308743i	$-0.900092\pi$
$317$	−1.07307	+	2.59063i	−0.0602698	+	0.145504i	0.890876	+	0.454247i	$0.150092\pi$
$318$		0			0
$319$	−17.1899			−0.962448
$320$	−5.31331	−	8.97099i	−0.297023	−	0.501494i
$321$		0			0
$322$	−6.40759	+	26.3975i	−0.357081	+	1.47108i
$323$	−2.30735	+	5.57043i	−0.128384	+	0.309947i
$324$		0			0
$325$	3.24890	−	1.34574i	0.180217	−	0.0746482i
$326$	2.86007	+	2.08895i	0.158405	+	0.115696i
$327$		0			0
$328$	4.42332	−	0.314634i	0.244237	−	0.0173728i
$329$	−8.18691	−	8.18691i	−0.451359	−	0.451359i
$330$		0			0
$331$	−1.37795	−	3.32667i	−0.0757390	−	0.182850i	0.881475	−	0.472230i	$-0.156551\pi$
$331$	−1.37795	−	3.32667i	−0.0757390	−	0.182850i	−0.957214	+	0.289380i	$0.906551\pi$
$332$	7.18192	+	8.49492i	0.394159	+	0.466219i
$333$		0			0
$334$	−3.75590	−	6.16374i	−0.205514	−	0.337265i
$335$		−	3.89544i		−	0.212830i
$336$		0			0
$337$			0.473748i			0.0258067i	0.999917	+	0.0129034i	$0.00410738\pi$
$337$			0.473748i			0.0258067i	−0.999917	+	0.0129034i	$0.995893\pi$
$338$	14.3294	−	8.73170i	0.779418	−	0.474942i
$339$		0			0
$340$	0.212994	−	2.54310i	0.0115512	−	0.137919i
$341$	−3.31502	−	8.00317i	−0.179518	−	0.433396i
$342$		0			0
$343$	1.40095	+	1.40095i	0.0756440	+	0.0756440i
$344$	−24.3388	−	8.11122i	−1.31226	−	0.437328i
$345$		0			0
$346$	−1.95881	+	2.68189i	−0.105306	+	0.144179i
$347$	9.36785	−	3.88029i	0.502893	−	0.208305i	−0.116791	−	0.993156i	$-0.537261\pi$
$347$	9.36785	−	3.88029i	0.502893	−	0.208305i	0.619684	+	0.784852i	$0.287261\pi$
$348$		0			0
$349$	−2.04231	+	4.93057i	−0.109322	+	0.263928i	−0.969068	−	0.246796i	$-0.920622\pi$
$349$	−2.04231	+	4.93057i	−0.109322	+	0.263928i	0.859745	+	0.510723i	$0.170622\pi$
$350$	−16.6458	−	4.04051i	−0.889755	−	0.215974i
$351$		0			0
$352$	22.1486	+	22.7116i	1.18053	+	1.21053i
$353$	−34.7185			−1.84788			−0.923939	−	0.382539i	$-0.875050\pi$
$353$	−34.7185			−1.84788			−0.923939	+	0.382539i	$0.875050\pi$
$354$		0			0
$355$	−7.07969	+	17.0919i	−0.375751	+	0.907144i
$356$	−16.5784	+	5.29480i	−0.878653	+	0.280624i
$357$		0			0
$358$	−2.40592	+	3.29405i	−0.127157	+	0.174096i
$359$	4.06394	−	4.06394i	0.214486	−	0.214486i	−0.591684	−	0.806170i	$-0.701537\pi$
$359$	4.06394	−	4.06394i	0.214486	−	0.214486i	0.806170	+	0.591684i	$0.201537\pi$
$360$		0			0
$361$	13.3825	+	13.3825i	0.704343	+	0.704343i
$362$	4.04887	−	0.630867i	0.212804	−	0.0331576i
$363$		0			0
$364$	7.78855	+	0.652321i	0.408231	+	0.0341909i
$365$	13.8118	+	5.72104i	0.722944	+	0.299453i
$366$		0			0
$367$		−	30.2747i		−	1.58033i	−0.612896	−	0.790164i	$-0.709996\pi$
$367$		−	30.2747i		−	1.58033i	0.612896	−	0.790164i	$-0.290004\pi$
$368$	−3.48351	+	20.6502i	−0.181591	+	1.07647i
$369$		0			0
$370$	−8.54735	−	14.0269i	−0.444356	−	0.729224i
$371$	22.6082	+	9.36463i	1.17376	+	0.486188i
$372$		0			0
$373$	8.46231	+	20.4298i	0.438162	+	1.05782i	0.976583	+	0.215141i	$0.0690210\pi$
$373$	8.46231	+	20.4298i	0.438162	+	1.05782i	−0.538421	+	0.842676i	$0.680979\pi$
$374$	1.19542	+	7.67217i	0.0618139	+	0.396718i
$375$		0			0
$376$	−6.74356	−	5.84792i	−0.347773	−	0.301583i
$377$	−2.30874	+	2.30874i	−0.118906	+	0.118906i
$378$		0			0
$379$	21.3128	−	8.82807i	1.09477	−	0.453467i	0.239100	−	0.970995i	$-0.423147\pi$
$379$	21.3128	−	8.82807i	1.09477	−	0.453467i	0.855667	+	0.517527i	$0.173147\pi$
$380$	−14.2661	−	7.35936i	−0.731835	−	0.377527i
$381$		0			0
$382$	2.78649	−	11.4796i	0.142569	−	0.587346i
$383$	25.5734			1.30674			0.653370	−	0.757039i	$-0.273355\pi$
$383$	25.5734			1.30674			0.653370	+	0.757039i	$0.273355\pi$
$384$		0			0
$385$	−26.8147			−1.36660
$386$	4.11486	−	16.9521i	0.209441	−	0.862839i
$387$		0			0
$388$	−25.5687	−	13.1900i	−1.29805	−	0.669619i
$389$	1.19642	−	0.495572i	0.0606608	−	0.0251265i	−0.352147	−	0.935945i	$-0.614548\pi$
$389$	1.19642	−	0.495572i	0.0606608	−	0.0251265i	0.412808	+	0.910818i	$0.364548\pi$
$390$		0			0
$391$	−3.62451	+	3.62451i	−0.183299	+	0.183299i
$392$	−13.8041	−	11.9707i	−0.697211	−	0.604611i
$393$		0			0
$394$	5.07042	+	32.5417i	0.255444	+	1.63943i
$395$	0.0775352	+	0.187187i	0.00390122	+	0.00941838i
$396$		0			0
$397$	5.47211	+	2.26662i	0.274637	+	0.113758i	0.515751	−	0.856738i	$-0.327513\pi$
$397$	5.47211	+	2.26662i	0.274637	+	0.113758i	−0.241114	+	0.970497i	$0.577513\pi$
$398$	−17.7269	−	29.0912i	−0.888567	−	1.45821i
$399$		0			0
$400$	−13.0217	−	2.19664i	−0.651083	−	0.109832i
$401$		−	33.2794i		−	1.66189i	−0.556352	−	0.830947i	$-0.687799\pi$
$401$		−	33.2794i		−	1.66189i	0.556352	−	0.830947i	$-0.312201\pi$
$402$		0			0
$403$	−1.52012	−	0.629655i	−0.0757227	−	0.0313654i
$404$	26.1453	+	2.18977i	1.30078	+	0.108945i
$405$		0			0
$406$	15.7143	−	2.44849i	0.779888	−	0.121517i
$407$	35.3395	+	35.3395i	1.75172	+	1.75172i
$408$		0			0
$409$	7.40530	−	7.40530i	0.366168	−	0.366168i	−0.499909	−	0.866078i	$-0.666633\pi$
$409$	7.40530	−	7.40530i	0.366168	−	0.366168i	0.866078	+	0.499909i	$0.166633\pi$
$410$	−1.70441	+	2.33358i	−0.0841747	+	0.115247i
$411$		0			0
$412$	27.7672	−	8.86829i	1.36799	−	0.436909i
$413$	13.6074	−	32.8511i	0.669575	−	1.61650i
$414$		0			0
$415$	−7.24896			−0.355838
$416$	6.02508	+	0.0756046i	0.295404	+	0.00370682i
$417$		0			0
$418$	47.4631	+	11.5209i	2.32150	+	0.563507i
$419$	6.43037	−	15.5243i	0.314144	−	0.758411i	−0.685399	−	0.728168i	$-0.740372\pi$
$419$	6.43037	−	15.5243i	0.314144	−	0.758411i	0.999543	−	0.0302425i	$-0.00962796\pi$
$420$		0			0
$421$	5.60807	−	2.32294i	0.273321	−	0.113213i	−0.241813	−	0.970323i	$-0.577742\pi$
$421$	5.60807	−	2.32294i	0.273321	−	0.113213i	0.515134	+	0.857110i	$0.327742\pi$
$422$	8.00419	−	10.9589i	0.389638	−	0.533470i
$423$		0			0
$424$	17.8980	+	5.96475i	0.869204	+	0.289674i
$425$	−2.28555	−	2.28555i	−0.110865	−	0.110865i
$426$		0			0
$427$	7.36385	+	17.7779i	0.356362	+	0.860334i
$428$	0.251613	−	3.00420i	0.0121622	−	0.145213i
$429$		0			0
$430$	14.2763	−	8.69930i	0.688462	−	0.419517i
$431$			0.297166i			0.0143140i	0.999974	+	0.00715698i	$0.00227816\pi$
$431$			0.297166i			0.0143140i	−0.999974	+	0.00715698i	$0.997722\pi$
$432$		0			0
$433$			15.4119i			0.740649i	0.928902	+	0.370325i	$0.120754\pi$
$433$			15.4119i			0.740649i	−0.928902	+	0.370325i	$0.879246\pi$
$434$	4.17042	+	6.84400i	0.200186	+	0.328522i
$435$		0			0
$436$	15.4772	+	18.3067i	0.741222	+	0.876732i
$437$	12.3386	+	29.7879i	0.590233	+	1.42495i
$438$		0			0
$439$	−3.15252	−	3.15252i	−0.150462	−	0.150462i	0.627863	−	0.778324i	$-0.283930\pi$
$439$	−3.15252	−	3.15252i	−0.150462	−	0.150462i	−0.778324	+	0.627863i	$0.783930\pi$
$440$	−20.6205	+	1.46675i	−0.983044	+	0.0699247i
$441$		0			0
$442$	1.19099	+	0.869878i	0.0566495	+	0.0413759i
$443$	−2.80647	+	1.16248i	−0.133339	+	0.0552310i	−0.448355	−	0.893855i	$-0.647990\pi$
$443$	−2.80647	+	1.16248i	−0.133339	+	0.0552310i	0.315016	+	0.949086i	$0.397990\pi$
$444$		0			0
$445$	4.33998	−	10.4776i	0.205735	−	0.496688i
$446$	−2.30504	+	9.49612i	−0.109147	+	0.449654i
$447$		0			0
$448$	−23.4824	−	17.6072i	−1.10944	−	0.831863i
$449$	3.57715			0.168816			0.0844080	−	0.996431i	$-0.473100\pi$
$449$	3.57715			0.168816			0.0844080	+	0.996431i	$0.473100\pi$
$450$		0			0
$451$	3.36469	−	8.12307i	0.158437	−	0.382500i
$452$	8.62943	−	16.7281i	0.405894	−	0.786825i
$453$		0			0
$454$	−4.92742	−	3.59891i	−0.231255	−	0.168905i
$455$	−3.60142	+	3.60142i	−0.168837	+	0.168837i
$456$		0			0
$457$	−8.97857	−	8.97857i	−0.420000	−	0.420000i	0.465204	−	0.885204i	$-0.345981\pi$
$457$	−8.97857	−	8.97857i	−0.420000	−	0.420000i	−0.885204	+	0.465204i	$0.845981\pi$
$458$	1.67103	+	10.7246i	0.0780823	+	0.501128i
$459$		0			0
$460$	−8.81073	−	10.4215i	−0.410802	−	0.485905i
$461$	26.0500	+	10.7903i	1.21327	+	0.502553i	0.895264	−	0.445536i	$-0.146987\pi$
$461$	26.0500	+	10.7903i	1.21327	+	0.502553i	0.318006	+	0.948089i	$0.396987\pi$
$462$		0			0
$463$		−	10.9782i		−	0.510199i	−0.966915	−	0.255100i	$-0.917892\pi$
$463$		−	10.9782i		−	0.510199i	0.966915	−	0.255100i	$-0.0821083\pi$
$464$	11.9504	−	2.74246i	0.554783	−	0.127316i
$465$		0			0
$466$	−2.55180	+	1.55495i	−0.118210	+	0.0720318i
$467$	−38.5388	−	15.9633i	−1.78336	−	0.738694i	−0.991829	−	0.127571i	$-0.959282\pi$
$467$	−38.5388	−	15.9633i	−1.78336	−	0.738694i	−0.791535	−	0.611123i	$-0.790718\pi$
$468$		0			0
$469$	−4.19636	−	10.1309i	−0.193770	−	0.467802i
$470$	5.74730	−	0.895503i	0.265103	−	0.0413065i
$471$		0			0
$472$	8.66714	−	26.0069i	0.398938	−	1.19706i
$473$	−35.9678	+	35.9678i	−1.65380	+	1.65380i
$474$		0			0
$475$	−18.7837	+	7.78047i	−0.861856	+	0.356992i
$476$	−2.18562	−	6.84332i	−0.100178	−	0.313663i
$477$		0			0
$478$	−7.43791	−	1.80544i	−0.340202	−	0.0825788i
$479$	−20.8426			−0.952324			−0.476162	−	0.879357i	$-0.657973\pi$
$479$	−20.8426			−0.952324			−0.476162	+	0.879357i	$0.657973\pi$
$480$		0			0
$481$	9.49276			0.432833
$482$	27.0304	+	6.56121i	1.23120	+	0.298855i
$483$		0			0
$484$	38.9599	−	12.4430i	1.77090	−	0.565590i
$485$	17.3211	−	7.17462i	0.786510	−	0.325783i
$486$		0			0
$487$	−16.3086	+	16.3086i	−0.739014	+	0.739014i	−0.972387	−	0.233373i	$-0.925024\pi$
$487$	−16.3086	+	16.3086i	−0.739014	+	0.739014i	0.233373	+	0.972387i	$0.425024\pi$
$488$	6.63526	+	13.2684i	0.300364	+	0.600634i
$489$		0			0
$490$	11.7647	−	1.83310i	0.531476	−	0.0828108i
$491$	2.22643	+	5.37508i	0.100477	+	0.242574i	0.966122	−	0.258084i	$-0.0830913\pi$
$491$	2.22643	+	5.37508i	0.100477	+	0.242574i	−0.865645	+	0.500658i	$0.833091\pi$
$492$		0			0
$493$	2.77261	+	1.14845i	0.124872	+	0.0517237i
$494$	7.92202	−	4.82732i	0.356429	−	0.217191i
$495$		0			0
$496$	3.58142	+	5.03492i	0.160811	+	0.226075i
$497$			52.0778i			2.33601i
$498$		0			0
$499$	9.39859	+	3.89302i	0.420739	+	0.174276i	0.583000	−	0.812472i	$-0.301879\pi$
$499$	9.39859	+	3.89302i	0.420739	+	0.174276i	−0.162261	+	0.986748i	$0.551879\pi$
$500$	16.5243	−	13.9703i	0.738991	−	0.624771i
$501$		0			0
$502$	−5.57693	−	35.7924i	−0.248910	−	1.59749i
$503$	−21.5760	−	21.5760i	−0.962027	−	0.962027i	0.0372777	−	0.999305i	$-0.488131\pi$
$503$	−21.5760	−	21.5760i	−0.962027	−	0.962027i	−0.999305	+	0.0372777i	$0.988131\pi$
$504$		0			0
$505$	−12.0896	+	12.0896i	−0.537979	+	0.537979i
$506$	33.5307	+	24.4903i	1.49062	+	1.08872i
$507$		0			0
$508$	−28.4778	−	14.6907i	−1.26350	−	0.651793i
$509$	−1.30560	+	3.15200i	−0.0578697	+	0.139710i	−0.950170	−	0.311733i	$-0.899091\pi$
$509$	−1.30560	+	3.15200i	−0.0578697	+	0.139710i	0.892300	+	0.451443i	$0.149091\pi$
$510$		0			0
$511$	42.0836			1.86167
$512$	−19.0211	−	12.2555i	−0.840623	−	0.541621i
$513$		0			0
$514$	−3.14992	+	12.9768i	−0.138937	+	0.572383i
$515$	−7.26906	+	17.5491i	−0.320313	+	0.773304i
$516$		0			0
$517$	−16.3506	+	6.77264i	−0.719099	+	0.297860i
$518$	−37.3397	−	27.2723i	−1.64061	−	1.19828i
$519$		0			0
$520$	−2.57250	+	2.96649i	−0.112812	+	0.130089i
$521$	−7.58009	−	7.58009i	−0.332090	−	0.332090i	0.521290	−	0.853380i	$-0.325451\pi$
$521$	−7.58009	−	7.58009i	−0.332090	−	0.332090i	−0.853380	+	0.521290i	$0.825451\pi$
$522$		0			0
$523$	−5.67736	−	13.7064i	−0.248254	−	0.599337i	0.749802	−	0.661662i	$-0.230149\pi$
$523$	−5.67736	−	13.7064i	−0.248254	−	0.599337i	−0.998056	+	0.0623246i	$0.980149\pi$
$524$	8.72522	−	7.37663i	0.381163	−	0.322250i
$525$		0			0
$526$	8.72939	+	14.3256i	0.380619	+	0.624628i
$527$			1.51233i			0.0658782i
$528$		0			0
$529$			4.41042i			0.191758i
$530$	−10.4983	+	6.39720i	−0.456019	+	0.277877i
$531$		0			0
$532$	−45.0299	−	3.77143i	−1.95229	−	0.163512i
$533$	−0.639089	−	1.54290i	−0.0276820	−	0.0668303i
$534$		0			0
$535$	1.38914	+	1.38914i	0.0600578	+	0.0600578i
$536$	−3.78117	−	7.56115i	−0.163322	−	0.326592i
$537$		0			0
$538$	0.0591441	−	0.0809768i	0.00254988	−	0.00349116i
$539$	−33.4697	+	13.8636i	−1.44164	+	0.597148i
$540$		0			0
$541$	−14.0508	+	33.9216i	−0.604090	+	1.45840i	0.265247	+	0.964181i	$0.414547\pi$
$541$	−14.0508	+	33.9216i	−0.604090	+	1.45840i	−0.869336	+	0.494221i	$0.835453\pi$
$542$	19.9105	+	4.83296i	0.855228	+	0.207593i
$543$		0			0
$544$	−2.05507	−	5.14297i	−0.0881104	−	0.220503i
$545$	−15.6217			−0.669158
$546$		0			0
$547$	7.85438	−	18.9622i	0.335829	−	0.810763i	−0.662278	−	0.749258i	$-0.730410\pi$
$547$	7.85438	−	18.9622i	0.335829	−	0.810763i	0.998107	−	0.0615046i	$-0.0195899\pi$
$548$	−7.43122	−	23.2677i	−0.317446	−	0.993945i
$549$		0			0
$550$	−15.4431	+	21.1438i	−0.658496	+	0.901576i
$551$	13.3481	−	13.3481i	0.568648	−	0.568648i
$552$		0			0
$553$	0.403294	+	0.403294i	0.0171498	+	0.0171498i
$554$	−29.8317	+	4.64817i	−1.26743	+	0.197482i
$555$		0			0
$556$	−1.76819	+	21.1117i	−0.0749878	+	0.895335i
$557$	20.1683	+	8.35400i	0.854560	+	0.353970i	0.766578	−	0.642152i	$-0.221958\pi$
$557$	20.1683	+	8.35400i	0.854560	+	0.353970i	0.0879825	+	0.996122i	$0.471958\pi$
$558$		0			0
$559$			9.66152i			0.408639i
$560$	18.6415	−	4.27799i	0.787749	−	0.180778i
$561$		0			0
$562$	−2.87520	−	4.71843i	−0.121283	−	0.199035i
$563$	21.3521	+	8.84433i	0.899884	+	0.372744i	0.784175	−	0.620539i	$-0.213086\pi$
$563$	21.3521	+	8.84433i	0.899884	+	0.372744i	0.115708	+	0.993283i	$0.463086\pi$
$564$		0			0
$565$	4.69395	+	11.3322i	0.197476	+	0.476749i
$566$	−1.38307	−	8.87646i	−0.0581346	−	0.373105i
$567$		0			0
$568$	2.84864	+	40.0479i	0.119526	+	1.68037i
$569$	7.60582	−	7.60582i	0.318853	−	0.318853i	−0.529474	−	0.848326i	$-0.677611\pi$
$569$	7.60582	−	7.60582i	0.318853	−	0.318853i	0.848326	+	0.529474i	$0.177611\pi$
$570$		0			0
$571$	0.616329	−	0.255292i	0.0257926	−	0.0106836i	−0.369750	−	0.929131i	$-0.620557\pi$
$571$	0.616329	−	0.255292i	0.0257926	−	0.0106836i	0.395542	+	0.918448i	$0.370557\pi$
$572$	5.47717	−	10.6175i	0.229012	−	0.443939i
$573$		0			0
$574$	−1.91883	+	7.90505i	−0.0800904	+	0.329950i
$575$	−17.2845			−0.720814
$576$		0			0
$577$	−8.78481			−0.365716			−0.182858	−	0.983139i	$-0.558535\pi$
$577$	−8.78481			−0.365716			−0.182858	+	0.983139i	$0.558535\pi$
$578$	−5.35129	+	22.0459i	−0.222584	+	0.916987i
$579$		0			0
$580$	−3.66303	+	7.10076i	−0.152099	+	0.294843i
$581$	−18.8525	+	7.80896i	−0.782133	+	0.323970i
$582$		0			0
$583$	26.4496	−	26.4496i	1.09543	−	1.09543i
$584$	32.3623	−	2.30196i	1.33916	−	0.0952558i
$585$		0			0
$586$	−1.06409	−	6.82925i	−0.0439570	−	0.282114i
$587$	10.5345	+	25.4324i	0.434803	+	1.04971i	0.977718	+	0.209921i	$0.0673206\pi$
$587$	10.5345	+	25.4324i	0.434803	+	1.04971i	−0.542915	+	0.839788i	$0.682679\pi$
$588$		0			0
$589$	8.78867	+	3.64039i	0.362131	+	0.150000i
$590$	9.29552	+	15.2547i	0.382691	+	0.628027i
$591$		0			0
$592$	−30.2061	−	18.9300i	−1.24146	−	0.778018i
$593$			12.6478i			0.519384i	0.965691	+	0.259692i	$0.0836211\pi$
$593$			12.6478i			0.519384i	−0.965691	+	0.259692i	$0.916379\pi$
$594$		0			0
$595$	4.32502	+	1.79148i	0.177309	+	0.0734436i
$596$	−0.482197	+	5.75731i	−0.0197516	+	0.235829i
$597$		0			0
$598$	7.79267	−	1.21420i	0.318666	−	0.0496523i
$599$	−10.2749	−	10.2749i	−0.419820	−	0.419820i	0.465322	−	0.885142i	$-0.345939\pi$
$599$	−10.2749	−	10.2749i	−0.419820	−	0.419820i	−0.885142	+	0.465322i	$0.845939\pi$
$600$		0			0
$601$	−34.4571	+	34.4571i	−1.40554	+	1.40554i	−0.624552	+	0.780983i	$0.714719\pi$
$601$	−34.4571	+	34.4571i	−1.40554	+	1.40554i	−0.780983	+	0.624552i	$0.785281\pi$
$602$	27.7572	−	38.0035i	1.13130	−	1.54891i
$603$		0			0
$604$	−5.51152	−	17.2569i	−0.224260	−	0.702175i
$605$	−10.1991	+	24.6229i	−0.414653	+	1.00106i
$606$		0			0
$607$	5.97427			0.242488			0.121244	−	0.992623i	$-0.461312\pi$
$607$	5.97427			0.242488			0.121244	+	0.992623i	$0.461312\pi$
$608$	−34.8344	−	0.437112i	−1.41272	−	0.0177272i
$609$		0			0
$610$	−9.39445	−	2.28036i	−0.380370	−	0.0923290i
$611$	−1.28640	+	3.10563i	−0.0520420	+	0.125641i
$612$		0			0
$613$	1.37874	−	0.571093i	0.0556868	−	0.0230662i	−0.354666	−	0.934993i	$-0.615405\pi$
$613$	1.37874	−	0.571093i	0.0556868	−	0.0230662i	0.410353	+	0.911927i	$0.365405\pi$
$614$	−7.62184	+	10.4354i	−0.307592	+	0.421138i
$615$		0			0
$616$	−52.0480	+	26.0281i	−2.09707	+	1.04870i
$617$	−20.4851	−	20.4851i	−0.824698	−	0.824698i	0.162080	−	0.986778i	$-0.448180\pi$
$617$	−20.4851	−	20.4851i	−0.824698	−	0.824698i	−0.986778	+	0.162080i	$0.948180\pi$
$618$		0			0
$619$	13.2969	+	32.1015i	0.534447	+	1.29027i	0.928552	+	0.371203i	$0.121055\pi$
$619$	13.2969	+	32.1015i	0.534447	+	1.29027i	−0.394105	+	0.919065i	$0.628945\pi$
$620$	−4.01234	−	0.336049i	−0.161139	−	0.0134961i
$621$		0			0
$622$	35.5992	−	21.6925i	1.42740	−	0.869792i
$623$		−	31.9246i		−	1.27903i
$624$		0			0
$625$		−	2.40633i		−	0.0962532i
$626$	14.6767	+	24.0857i	0.586601	+	0.962660i
$627$		0			0
$628$	11.4034	−	9.64086i	0.455045	−	0.384712i
$629$	−3.33900	−	8.06106i	−0.133135	−	0.321415i
$630$		0			0
$631$	2.04327	+	2.04327i	0.0813412	+	0.0813412i	0.746607	−	0.665266i	$-0.231682\pi$
$631$	2.04327	+	2.04327i	0.0813412	+	0.0813412i	−0.665266	+	0.746607i	$0.731682\pi$
$632$	0.332194	+	0.288074i	0.0132140	+	0.0114590i
$633$		0			0
$634$	−3.20235	−	2.33894i	−0.127181	−	0.0928912i
$635$	19.2918	−	7.99093i	0.765572	−	0.317110i
$636$		0			0
$637$	−2.63325	+	6.35724i	−0.104333	+	0.251883i
$638$	5.73440	−	23.6242i	0.227027	−	0.935289i
$639$		0			0
$640$	14.1014	−	4.30947i	0.557405	−	0.170347i
$641$	20.3790			0.804922			0.402461	−	0.915437i	$-0.368155\pi$
$641$	20.3790			0.804922			0.402461	+	0.915437i	$0.368155\pi$
$642$		0			0
$643$	4.75816	−	11.4872i	0.187644	−	0.453012i	−0.801861	−	0.597510i	$-0.796157\pi$
$643$	4.75816	−	11.4872i	0.187644	−	0.453012i	0.989505	+	0.144498i	$0.0461568\pi$
$644$	−34.1408	−	17.6120i	−1.34533	−	0.694010i
$645$		0			0
$646$	−6.88576	−	5.02925i	−0.270917	−	0.197873i
$647$	−8.97597	+	8.97597i	−0.352882	+	0.352882i	−0.861181	−	0.508299i	$-0.830274\pi$
$647$	−8.97597	+	8.97597i	−0.352882	+	0.352882i	0.508299	+	0.861181i	$0.330274\pi$
$648$		0			0
$649$	−38.4329	−	38.4329i	−1.50862	−	1.50862i
$650$	0.765651	+	4.91391i	0.0300313	+	0.192740i
$651$		0			0
$652$	−3.82495	+	3.23375i	−0.149797	+	0.126644i
$653$	−42.2027	−	17.4809i	−1.65152	−	0.684082i	−0.654136	−	0.756377i	$-0.726968\pi$
$653$	−42.2027	−	17.4809i	−1.65152	−	0.684082i	−0.997383	+	0.0722952i	$0.976968\pi$
$654$		0			0
$655$			7.44549i			0.290919i
$656$	−1.04318	+	6.18395i	−0.0407293	+	0.241443i
$657$		0			0
$658$	13.9824	−	8.52023i	0.545091	−	0.332153i
$659$	−5.50356	−	2.27965i	−0.214388	−	0.0888025i	0.272905	−	0.962041i	$-0.412016\pi$
$659$	−5.50356	−	2.27965i	−0.214388	−	0.0888025i	−0.487293	+	0.873239i	$0.662016\pi$
$660$		0			0
$661$	−17.5581	−	42.3890i	−0.682931	−	1.64874i	−0.758557	−	0.651606i	$-0.774095\pi$
$661$	−17.5581	−	42.3890i	−0.682931	−	1.64874i	0.0756260	−	0.997136i	$-0.475905\pi$
$662$	5.03153	−	0.783978i	0.195556	−	0.0304702i
$663$		0			0
$664$	−14.0704	+	7.03632i	−0.546039	+	0.273062i
$665$	20.8218	−	20.8218i	0.807436	−	0.807436i
$666$		0			0
$667$	14.8266	−	6.14136i	0.574087	−	0.237795i
$668$	9.72379	−	3.10558i	0.376225	−	0.120159i
$669$		0			0
$670$	5.35352	+	1.29948i	0.206824	+	0.0502034i
$671$	29.4137			1.13550
$672$		0			0
$673$	−14.4979			−0.558853			−0.279427	−	0.960167i	$-0.590144\pi$
$673$	−14.4979			−0.558853			−0.279427	+	0.960167i	$0.590144\pi$
$674$	−0.651075	−	0.158038i	−0.0250785	−	0.00608741i
$675$		0			0
$676$	7.21985	+	22.6058i	0.277687	+	0.869456i
$677$	11.0022	−	4.55726i	0.422849	−	0.175150i	−0.161104	−	0.986937i	$-0.551505\pi$
$677$	11.0022	−	4.55726i	0.422849	−	0.175150i	0.583953	+	0.811788i	$0.301505\pi$
$678$		0			0
$679$	37.3183	−	37.3183i	1.43215	−	1.43215i
$680$	3.42394	+	1.14107i	0.131302	+	0.0437582i
$681$		0			0
$682$	12.1047	−	1.88606i	0.463511	−	0.0722211i
$683$	3.03396	+	7.32464i	0.116091	+	0.280269i	0.971236	−	0.238121i	$-0.0765314\pi$
$683$	3.03396	+	7.32464i	0.116091	+	0.280269i	−0.855144	+	0.518390i	$0.826531\pi$
$684$		0			0
$685$	14.7053	+	6.09114i	0.561861	+	0.232730i
$686$	−2.39267	+	1.45799i	−0.0913527	+	0.0556662i
$687$		0			0
$688$	19.2665	−	30.7431i	0.734529	−	1.17207i
$689$		−	7.10479i		−	0.270671i
$690$		0			0
$691$	−21.8871	−	9.06592i	−0.832623	−	0.344884i	−0.0746825	−	0.997207i	$-0.523794\pi$
$691$	−21.8871	−	9.06592i	−0.832623	−	0.344884i	−0.757941	+	0.652324i	$0.773794\pi$
$692$	−3.03229	−	3.58666i	−0.115270	−	0.136344i
$693$		0			0
$694$	2.20767	+	14.1687i	0.0838021	+	0.537837i
$695$	−9.76203	−	9.76203i	−0.370295	−	0.370295i
$696$		0			0
$697$	−1.08540	+	1.08540i	−0.0411125	+	0.0411125i
$698$	−6.09482	−	4.45156i	−0.230692	−	0.168494i
$699$		0			0
$700$	11.1058	−	21.5285i	0.419760	−	0.813702i
$701$	−18.8146	+	45.4224i	−0.710617	+	1.71558i	−0.0121647	+	0.999926i	$0.503872\pi$
$701$	−18.8146	+	45.4224i	−0.710617	+	1.71558i	−0.698453	+	0.715656i	$0.746128\pi$
$702$		0			0
$703$	−54.8829			−2.06995
$704$	−38.6012	+	22.8626i	−1.45484	+	0.861668i
$705$		0			0
$706$	11.5818	−	47.7138i	0.435886	−	1.79573i
$707$	−18.4180	+	44.4650i	−0.692681	+	1.67228i
$708$		0			0
$709$	−22.5420	+	9.33718i	−0.846581	+	0.350665i	−0.763445	−	0.645873i	$-0.776494\pi$
$709$	−22.5420	+	9.33718i	−0.846581	+	0.350665i	−0.0831359	+	0.996538i	$0.526494\pi$
$710$	−21.1278	−	15.4314i	−0.792911	−	0.579129i
$711$		0			0
$712$	−1.74627	−	24.5501i	−0.0654442	−	0.920053i
$713$	5.71852	+	5.71852i	0.214160	+	0.214160i
$714$		0			0
$715$	2.97928	+	7.19263i	0.111419	+	0.268989i
$716$	−3.72444	−	4.40534i	−0.139189	−	0.164635i
$717$		0			0
$718$	4.22940	+	6.94078i	0.157840	+	0.259028i
$719$		−	38.2799i		−	1.42760i	−0.700350	−	0.713800i	$-0.746973\pi$
$719$		−	38.2799i		−	1.42760i	0.700350	−	0.713800i	$-0.253027\pi$
$720$		0			0
$721$			53.4707i			1.99135i
$722$	−22.8560	+	13.9274i	−0.850611	+	0.518323i
$723$		0			0
$724$	−0.483665	+	5.77484i	−0.0179753	+	0.214620i
$725$	3.87263	+	9.34936i	0.143826	+	0.347226i
$726$		0			0
$727$	−2.75063	−	2.75063i	−0.102015	−	0.102015i	0.654257	−	0.756272i	$-0.272981\pi$
$727$	−2.75063	−	2.75063i	−0.102015	−	0.102015i	−0.756272	+	0.654257i	$0.772981\pi$
$728$	−3.49468	+	10.4862i	−0.129522	+	0.388646i
$729$		0			0
$730$	−12.4700	+	17.0732i	−0.461534	+	0.631906i
$731$	8.20436	−	3.39836i	0.303449	−	0.125693i
$732$		0			0
$733$	−6.75290	+	16.3029i	−0.249424	+	0.602163i	−0.998155	−	0.0607106i	$-0.980663\pi$
$733$	−6.75290	+	16.3029i	−0.249424	+	0.602163i	0.748731	+	0.662874i	$0.230663\pi$
$734$	41.6067	+	10.0994i	1.53573	+	0.372775i
$735$		0			0
$736$	−27.2177	−	11.6761i	−1.00326	−	0.430389i
$737$	−16.7617			−0.617424
$738$		0			0
$739$	9.62421	−	23.2349i	0.354032	−	0.854709i	−0.642082	−	0.766636i	$-0.721929\pi$
$739$	9.62421	−	23.2349i	0.354032	−	0.854709i	0.996114	−	0.0880732i	$-0.0280709\pi$
$740$	22.1286	−	7.06742i	0.813463	−	0.259803i
$741$		0			0
$742$	−20.4118	+	27.9467i	−0.749340	+	1.02595i
$743$	32.2711	−	32.2711i	1.18391	−	1.18391i	0.205192	−	0.978722i	$-0.434218\pi$
$743$	32.2711	−	32.2711i	1.18391	−	1.18391i	0.978722	−	0.205192i	$-0.0657817\pi$
$744$		0			0
$745$	−2.66218	−	2.66218i	−0.0975347	−	0.0975347i
$746$	−30.8998	+	4.81459i	−1.13132	+	0.176275i
$747$		0			0
$748$	−10.9427	−	0.916493i	−0.400104	−	0.0335103i
$749$	5.10921	+	2.11630i	0.186687	+	0.0773281i
$750$		0			0
$751$			2.67256i			0.0975231i	0.998810	+	0.0487616i	$0.0155274\pi$
$751$			2.67256i			0.0975231i	−0.998810	+	0.0487616i	$0.984473\pi$
$752$	10.2864	−	7.31690i	0.375107	−	0.266820i
$753$		0			0
$754$	−2.40274	−	3.94309i	−0.0875025	−	0.143599i
$755$	10.9065	+	4.51762i	0.396928	+	0.164413i
$756$		0			0
$757$	−9.38519	−	22.6579i	−0.341111	−	0.823514i	−0.997604	−	0.0691822i	$-0.977961\pi$
$757$	−9.38519	−	22.6579i	−0.341111	−	0.823514i	0.656493	−	0.754332i	$-0.272039\pi$
$758$	5.02268	+	32.2353i	0.182432	+	1.17084i
$759$		0			0
$760$	14.8731	−	17.1510i	0.539502	−	0.622130i
$761$	12.8473	−	12.8473i	0.465714	−	0.465714i	−0.434809	−	0.900523i	$-0.643184\pi$
$761$	12.8473	−	12.8473i	0.465714	−	0.465714i	0.900523	+	0.434809i	$0.143184\pi$
$762$		0			0
$763$	−40.6275	+	16.8285i	−1.47081	+	0.609231i
$764$	14.8469	+	7.65898i	0.537142	+	0.277092i
$765$		0			0
$766$	−8.53106	+	35.1457i	−0.308240	+	1.26986i
$767$	−10.3237			−0.372767
$768$		0			0
$769$	15.9481			0.575102			0.287551	−	0.957765i	$-0.407159\pi$
$769$	15.9481			0.575102			0.287551	+	0.957765i	$0.407159\pi$
$770$	8.94514	−	36.8515i	0.322361	−	1.32804i
$771$		0			0
$772$	21.9247	+	11.3101i	0.789086	+	0.407061i
$773$	−4.77420	+	1.97754i	−0.171716	+	0.0711271i	−0.466885	−	0.884318i	$-0.654624\pi$
$773$	−4.77420	+	1.97754i	−0.171716	+	0.0711271i	0.295169	+	0.955445i	$0.404624\pi$
$774$		0			0
$775$	−3.60599	+	3.60599i	−0.129531	+	0.129531i
$776$	26.6565	−	30.7391i	0.956914	−	1.10347i
$777$		0			0
$778$	0.281953	+	1.80956i	0.0101085	+	0.0648760i
$779$	3.69493	+	8.92034i	0.132385	+	0.319604i
$780$		0			0
$781$	73.5447	+	30.4632i	2.63164	+	1.09006i
$782$	−3.77208	−	6.19029i	−0.134889	−	0.221364i
$783$		0			0
$784$	21.0563	−	14.9777i	0.752011	−	0.534918i
$785$			9.73086i			0.347309i
$786$		0			0
$787$	−14.1033	−	5.84179i	−0.502730	−	0.208237i	0.116882	−	0.993146i	$-0.462710\pi$
$787$	−14.1033	−	5.84179i	−0.502730	−	0.208237i	−0.619612	+	0.784908i	$0.712710\pi$
$788$	−46.4137	−	3.88733i	−1.65342	−	0.138480i
$789$		0			0
$790$	−0.283117	+	0.0441133i	−0.0100728	+	0.00156948i
$791$	24.4152	+	24.4152i	0.868106	+	0.868106i
$792$		0			0
$793$	3.95049	−	3.95049i	0.140286	−	0.140286i
$794$	−4.94048	+	6.76422i	−0.175331	+	0.240053i
$795$		0			0
$796$	45.8938	−	14.6575i	1.62666	−	0.519523i
$797$	15.7714	−	38.0755i	0.558652	−	1.34870i	−0.352182	−	0.935931i	$-0.614560\pi$
$797$	15.7714	−	38.0755i	0.558652	−	1.34870i	0.910834	−	0.412773i	$-0.135440\pi$
$798$		0			0
$799$	3.08972			0.109306
$800$	7.36276	−	17.1630i	0.260313	−	0.606802i
$801$		0			0
$802$	45.7361	+	11.1017i	1.61500	+	0.392015i
$803$	24.6171	−	59.4308i	0.868717	−	2.09727i
$804$		0			0
$805$	23.1281	−	9.57997i	0.815158	−	0.337650i
$806$	1.37244	−	1.87907i	0.0483421	−	0.0661872i
$807$		0			0
$808$	−11.7313	+	35.2011i	−0.412704	+	1.23837i
$809$	22.3087	+	22.3087i	0.784333	+	0.784333i	0.980559	−	0.196226i	$-0.0628685\pi$
$809$	22.3087	+	22.3087i	0.784333	+	0.784333i	−0.196226	+	0.980559i	$0.562869\pi$
$810$		0			0
$811$	−17.0179	−	41.0848i	−0.597579	−	1.44268i	−0.876041	−	0.482236i	$-0.839825\pi$
$811$	−17.0179	−	41.0848i	−0.597579	−	1.44268i	0.278462	−	0.960447i	$-0.410175\pi$
$812$	−1.87718	+	22.4131i	−0.0658762	+	0.786545i
$813$		0			0
$814$	−60.3563	+	36.7784i	−2.11549	+	1.28908i
$815$		−	3.26394i		−	0.114331i
$816$		0			0
$817$		−	55.8586i		−	1.95425i
$818$	7.70680	+	12.6475i	0.269462	+	0.442209i
$819$		0			0
$820$	−2.63848	−	3.12084i	−0.0921395	−	0.108984i
$821$	−4.17316	−	10.0749i	−0.145644	−	0.351616i	0.834176	−	0.551499i	$-0.185944\pi$
$821$	−4.17316	−	10.0749i	−0.145644	−	0.351616i	−0.979820	+	0.199883i	$0.935944\pi$
$822$		0			0
$823$	−21.0647	−	21.0647i	−0.734269	−	0.734269i	0.237194	−	0.971462i	$-0.423772\pi$
$823$	−21.0647	−	21.0647i	−0.734269	−	0.734269i	−0.971462	+	0.237194i	$0.923772\pi$
$824$	2.92483	+	41.1190i	0.101891	+	1.43245i
$825$		0			0
$826$	40.6082	+	29.6596i	1.41294	+	1.03199i
$827$	51.5584	−	21.3562i	1.79286	−	0.742627i	0.803840	−	0.594845i	$-0.202787\pi$
$827$	51.5584	−	21.3562i	1.79286	−	0.742627i	0.989020	−	0.147782i	$-0.0472134\pi$
$828$		0			0
$829$	12.1450	−	29.3206i	0.421813	−	1.01835i	−0.560000	−	0.828493i	$-0.689199\pi$
$829$	12.1450	−	29.3206i	0.421813	−	1.01835i	0.981812	−	0.189853i	$-0.0608013\pi$
$830$	2.41819	−	9.96229i	0.0839367	−	0.345796i
$831$		0			0
$832$	−2.11382	+	8.25508i	−0.0732835	+	0.286194i
$833$	6.32466			0.219136
$834$		0			0
$835$	−2.54555	+	6.14550i	−0.0880924	+	0.212674i
$836$	−31.6666	+	61.3855i	−1.09521	+	2.12306i
$837$		0			0
$838$	19.1900	+	14.0161i	0.662907	+	0.484177i
$839$	−21.1653	+	21.1653i	−0.730706	+	0.730706i	−0.970760	−	0.240054i	$-0.922835\pi$
$839$	−21.1653	+	21.1653i	−0.730706	+	0.730706i	0.240054	+	0.970760i	$0.422835\pi$
$840$		0			0
$841$	13.8623	+	13.8623i	0.478009	+	0.478009i
$842$	1.32162	+	8.48212i	0.0455462	+	0.292313i
$843$		0			0
$844$	12.3907	+	14.6560i	0.426506	+	0.504480i
$845$	−14.2870	−	5.91788i	−0.491489	−	0.203581i
$846$		0			0
$847$			75.0241i			2.57786i
$848$	−14.1680	+	22.6075i	−0.486532	+	0.776346i
$849$		0			0
$850$	3.90348	−	2.37860i	0.133888	−	0.0815854i
$851$	−43.1066	−	17.8553i	−1.47767	−	0.612073i
$852$		0			0
$853$	6.84996	+	16.5373i	0.234538	+	0.566225i	0.996701	−	0.0811601i	$-0.0258625\pi$
$853$	6.84996	+	16.5373i	0.234538	+	0.566225i	−0.762163	+	0.647385i	$0.775863\pi$
$854$	−26.8888	+	4.18963i	−0.920116	+	0.143366i
$855$		0			0
$856$	4.04475	+	1.34797i	0.138247	+	0.0460726i
$857$	33.6370	−	33.6370i	1.14902	−	1.14902i	0.162272	−	0.986746i	$-0.448118\pi$
$857$	33.6370	−	33.6370i	1.14902	−	1.14902i	0.986746	−	0.162272i	$-0.0518822\pi$
$858$		0			0
$859$	35.7350	−	14.8019i	1.21926	−	0.505035i	0.322088	−	0.946710i	$-0.395615\pi$
$859$	35.7350	−	14.8019i	1.21926	−	0.505035i	0.897175	+	0.441674i	$0.145615\pi$
$860$	7.19306	+	22.5220i	0.245281	+	0.767992i
$861$		0			0
$862$	−0.408396	−	0.0991319i	−0.0139100	−	0.00337645i
$863$	−44.4296			−1.51240			−0.756201	−	0.654340i	$-0.772947\pi$
$863$	−44.4296			−1.51240			−0.756201	+	0.654340i	$0.772947\pi$
$864$		0			0
$865$	3.06060			0.104064
$866$	−21.1807	−	5.14128i	−0.719749	−	0.174708i
$867$		0			0
$868$	−10.7970	+	3.44833i	−0.366473	+	0.117044i
$869$	0.805445	−	0.333626i	0.0273228	−	0.0113175i
$870$		0			0
$871$	−2.25122	+	2.25122i	−0.0762798	+	0.0762798i
$872$	−30.3221	+	15.1634i	−1.02683	+	0.513498i
$873$		0			0
$874$	−45.0538	+	7.01996i	−1.52397	+	0.237454i
$875$	15.1900	+	36.6719i	0.513516	+	1.23974i
$876$		0			0
$877$	31.7336	+	13.1445i	1.07157	+	0.443857i	0.847543	−	0.530727i	$-0.178081\pi$
$877$	31.7336	+	13.1445i	1.07157	+	0.443857i	0.224023	+	0.974584i	$0.428081\pi$
$878$	5.38418	−	3.28087i	0.181707	−	0.110724i
$879$		0			0
$880$	4.86306	−	28.8282i	0.163934	−	0.971798i
$881$		−	42.6814i		−	1.43797i	−0.695023	−	0.718987i	$-0.744606\pi$
$881$		−	42.6814i		−	1.43797i	0.695023	−	0.718987i	$-0.255394\pi$
$882$		0			0
$883$	22.4520	+	9.29994i	0.755571	+	0.312968i	0.727012	−	0.686624i	$-0.240908\pi$
$883$	22.4520	+	9.29994i	0.755571	+	0.312968i	0.0285587	+	0.999592i	$0.490908\pi$
$884$	−1.59278	+	1.34660i	−0.0535710	+	0.0452910i
$885$		0			0
$886$	−0.661386	−	4.24474i	−0.0222197	−	0.142605i
$887$	25.1413	+	25.1413i	0.844161	+	0.844161i	0.989397	−	0.145236i	$-0.0463941\pi$
$887$	25.1413	+	25.1413i	0.844161	+	0.844161i	−0.145236	+	0.989397i	$0.546394\pi$
$888$		0			0
$889$	41.5643	−	41.5643i	1.39402	−	1.39402i
$890$	12.9517	+	9.45972i	0.434142	+	0.317091i
$891$		0			0
$892$	−12.2816	−	6.33565i	−0.411220	−	0.212133i
$893$	7.43737	−	17.9554i	0.248882	−	0.600855i
$894$		0			0
$895$	3.75920			0.125656
$896$	32.0312	−	26.3984i	1.07009	−	0.881909i
$897$		0			0
$898$	−1.19331	+	4.91609i	−0.0398211	+	0.164052i
$899$	1.81196	−	4.37445i	0.0604321	−	0.145896i
$900$		0			0
$901$	−6.03324	+	2.49905i	−0.200996	+	0.0832554i
$902$	10.0412	+	7.33389i	0.334334	+	0.244192i
$903$		0			0
$904$	20.1108	+	17.4398i	0.668877	+	0.580040i
$905$	−2.67028	−	2.67028i	−0.0887632	−	0.0887632i
$906$		0			0
$907$	14.9664	+	36.1321i	0.496951	+	1.19975i	0.951118	+	0.308829i	$0.0999371\pi$
$907$	14.9664	+	36.1321i	0.496951	+	1.19975i	−0.454167	+	0.890917i	$0.650063\pi$
$908$	6.58974	−	5.57121i	0.218688	−	0.184887i
$909$		0			0
$910$	−3.74805	−	6.15086i	−0.124247	−	0.203899i
$911$			23.3974i			0.775190i	0.921830	+	0.387595i	$0.126694\pi$
$911$			23.3974i			0.775190i	−0.921830	+	0.387595i	$0.873306\pi$
$912$		0			0
$913$			31.1915i			1.03229i
$914$	15.3345	−	9.34413i	0.507220	−	0.309076i
$915$		0			0
$916$	−15.2963	−	1.28113i	−0.505405	−	0.0423297i
$917$	8.02067	+	19.3636i	0.264866	+	0.639442i
$918$		0			0
$919$	20.8473	+	20.8473i	0.687689	+	0.687689i	0.961721	−	0.274032i	$-0.0883574\pi$
$919$	20.8473	+	20.8473i	0.687689	+	0.687689i	−0.274032	+	0.961721i	$0.588357\pi$
$920$	17.2615	−	8.63211i	0.569095	−	0.284592i
$921$		0			0
$922$	−23.5192	+	32.2011i	−0.774563	+	1.06049i
$923$	13.9691	−	5.78618i	0.459798	−	0.190455i
$924$		0			0
$925$	11.2592	−	27.1822i	0.370202	−	0.893746i
$926$	15.0874	+	3.66223i	0.495802	+	0.120348i
$927$		0			0
$928$	−0.217567	+	17.3384i	−0.00714199	+	0.569160i
$929$	−55.9215			−1.83472			−0.917362	−	0.398055i	$-0.869685\pi$
$929$	−55.9215			−1.83472			−0.917362	+	0.398055i	$0.869685\pi$
$930$		0			0
$931$	15.2243	−	36.7547i	0.498956	−	1.20459i
$932$	−1.28572	−	4.02568i	−0.0421152	−	0.131865i
$933$		0			0
$934$	34.7947	−	47.6389i	1.13852	−	1.55879i
$935$	5.05989	−	5.05989i	0.165476	−	0.165476i
$936$		0			0
$937$	31.6178	+	31.6178i	1.03291	+	1.03291i	0.999440	+	0.0334692i	$0.0106556\pi$
$937$	31.6178	+	31.6178i	1.03291	+	1.03291i	0.0334692	+	0.999440i	$0.489344\pi$
$938$	15.3229	−	2.38750i	0.500309	−	0.0779546i
$939$		0			0
$940$	−0.686554	+	8.19727i	−0.0223929	+	0.267366i
$941$	−23.4212	−	9.70137i	−0.763509	−	0.316256i	−0.0332688	−	0.999446i	$-0.510592\pi$
$941$	−23.4212	−	9.70137i	−0.763509	−	0.316256i	−0.730240	+	0.683191i	$0.760592\pi$
$942$		0			0
$943$			8.20837i			0.267301i
$944$	32.8501	+	20.5870i	1.06918	+	0.670049i
$945$		0			0
$946$	−37.4322	−	61.4293i	−1.21703	−	1.99724i
$947$	−30.2016	−	12.5099i	−0.981419	−	0.406517i	−0.166468	−	0.986047i	$-0.553236\pi$
$947$	−30.2016	−	12.5099i	−0.981419	−	0.406517i	−0.814951	+	0.579530i	$0.803236\pi$
$948$		0			0
$949$	−4.67577	−	11.2883i	−0.151782	−	0.366434i
$950$	−4.42666	−	28.4101i	−0.143620	−	0.921744i
$951$		0			0
$952$	10.1339	−	0.720834i	0.328442	−	0.0233624i
$953$	17.7752	−	17.7752i	0.575795	−	0.575795i	−0.357947	−	0.933742i	$-0.616523\pi$
$953$	17.7752	−	17.7752i	0.575795	−	0.575795i	0.933742	+	0.357947i	$0.116523\pi$
$954$		0			0
$955$	−10.0578	+	4.16607i	−0.325462	+	0.134811i
$956$	4.96245	−	9.61969i	0.160497	−	0.311123i
$957$		0			0
$958$	6.95293	−	28.6442i	0.224639	−	0.925451i
$959$	44.8060			1.44686
$960$		0			0
$961$	−28.6139			−0.923030
$962$	−3.16670	+	13.0460i	−0.102099	+	0.420619i
$963$		0			0
$964$	−18.0342	+	34.9592i	−0.580843	+	1.12596i
$965$	−14.8525	+	6.15211i	−0.478119	+	0.198043i
$966$		0			0
$967$	5.23073	−	5.23073i	0.168209	−	0.168209i	−0.617983	−	0.786192i	$-0.712050\pi$
$967$	5.23073	−	5.23073i	0.168209	−	0.168209i	0.786192	+	0.617983i	$0.212050\pi$
$968$	4.10380	+	57.6936i	0.131901	+	1.85434i
$969$		0			0
$970$	4.08197	+	26.1979i	0.131064	+	0.841162i
$971$	−6.01158	−	14.5132i	−0.192921	−	0.465752i	0.797588	−	0.603203i	$-0.206109\pi$
$971$	−6.01158	−	14.5132i	−0.192921	−	0.465752i	−0.990509	+	0.137451i	$0.956109\pi$
$972$		0			0
$973$	−35.9044	−	14.8721i	−1.15104	−	0.476778i
$974$	−16.9726	−	27.8535i	−0.543838	−	0.892482i
$975$		0			0
$976$	−20.4484	+	4.69264i	−0.654536	+	0.150208i
$977$			48.6725i			1.55717i	0.627539	+	0.778585i	$0.284062\pi$
$977$			48.6725i			1.55717i	−0.627539	+	0.778585i	$0.715938\pi$
$978$		0			0
$979$	−45.0842	−	18.6745i	−1.44090	−	0.596840i
$980$	−1.40538	+	16.7798i	−0.0448931	+	0.536012i
$981$		0			0
$982$	−8.12973	+	1.26672i	−0.259430	+	0.0404226i
$983$	−7.17484	−	7.17484i	−0.228842	−	0.228842i	0.583367	−	0.812209i	$-0.301735\pi$
$983$	−7.17484	−	7.17484i	−0.228842	−	0.228842i	−0.812209	+	0.583367i	$0.801735\pi$
$984$		0			0
$985$	21.4617	−	21.4617i	0.683826	−	0.683826i
$986$	−2.50324	+	3.42730i	−0.0797195	+	0.109147i
$987$		0			0
$988$	3.99149	+	12.4976i	0.126986	+	0.397603i
$989$	18.1727	−	43.8729i	0.577860	−	1.39508i
$990$		0			0
$991$	−20.8957			−0.663774			−0.331887	−	0.943319i	$-0.607685\pi$
$991$	−20.8957			−0.663774			−0.331887	+	0.943319i	$0.607685\pi$
$992$	−8.11425	+	3.24236i	−0.257628	+	0.102945i
$993$		0			0
$994$	−71.5708	−	17.3727i	−2.27009	−	0.551029i
$995$	−12.0143	+	29.0051i	−0.380880	+	0.919525i
$996$		0			0
$997$	−48.3465	+	20.0258i	−1.53115	+	0.634223i	−0.979787	−	0.200042i	$-0.935892\pi$
$997$	−48.3465	+	20.0258i	−1.53115	+	0.634223i	−0.551363	+	0.834266i	$0.685892\pi$
$998$	−8.48550	+	11.6179i	−0.268604	+	0.367757i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.109.5		32
3.2	odd	2		96.2.n.a.13.4	✓	32
4.3	odd	2		1152.2.v.c.145.5		32
12.11	even	2		384.2.n.a.145.2		32
24.5	odd	2		768.2.n.a.289.3		32
24.11	even	2		768.2.n.b.289.7		32
32.5	even	8	inner	288.2.v.d.37.5		32
32.27	odd	8		1152.2.v.c.1009.5		32
96.5	odd	8		96.2.n.a.37.4	yes	32
96.11	even	8		768.2.n.b.481.7		32
96.53	odd	8		768.2.n.a.481.3		32
96.59	even	8		384.2.n.a.241.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.4	✓	32	3.2	odd	2
96.2.n.a.37.4	yes	32	96.5	odd	8
288.2.v.d.37.5		32	32.5	even	8	inner
288.2.v.d.109.5		32	1.1	even	1	trivial
384.2.n.a.145.2		32	12.11	even	2
384.2.n.a.241.2		32	96.59	even	8
768.2.n.a.289.3		32	24.5	odd	2
768.2.n.a.481.3		32	96.53	odd	8
768.2.n.b.289.7		32	24.11	even	2
768.2.n.b.481.7		32	96.11	even	8
1152.2.v.c.145.5		32	4.3	odd	2
1152.2.v.c.1009.5		32	32.27	odd	8

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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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.333592 + 1.37431i) q^{2} +(-1.77743 - 0.916914i) q^{4} +(1.20409 - 0.498752i) q^{5} +(2.59422 - 2.59422i) q^{7} +(1.85306 - 2.13686i) q^{8} +O(q^{10})\)	\(q+(-0.333592 + 1.37431i) q^{2} +(-1.77743 - 0.916914i) q^{4} +(1.20409 - 0.498752i) q^{5} +(2.59422 - 2.59422i) q^{7} +(1.85306 - 2.13686i) q^{8} +(0.283762 + 1.82117i) q^{10} +(-2.14608 - 5.18109i) q^{11} +(-0.984096 - 0.407626i) q^{13} +(2.69984 + 4.43066i) q^{14} +(2.31854 + 3.25951i) q^{16} +0.979053i q^{17} +(5.68961 + 2.35671i) q^{19} +(-2.59751 - 0.217551i) q^{20} +(7.83631 - 1.22100i) q^{22} +(3.70206 + 3.70206i) q^{23} +(-2.33445 + 2.33445i) q^{25} +(0.888489 - 1.21647i) q^{26} +(-6.98973 + 2.23238i) q^{28} +(1.17302 - 2.83193i) q^{29} +1.54469 q^{31} +(-5.25300 + 2.09904i) q^{32} +(-1.34552 - 0.326604i) q^{34} +(1.82981 - 4.41756i) q^{35} +(-8.23352 + 3.41044i) q^{37} +(-5.13685 + 7.03308i) q^{38} +(1.16549 - 3.49720i) q^{40} +(1.10862 + 1.10862i) q^{41} +(-3.47106 - 8.37989i) q^{43} +(-0.936101 + 11.1768i) q^{44} +(-6.32273 + 3.85278i) q^{46} -3.15582i q^{47} -6.45997i q^{49} +(-2.42949 - 3.98700i) q^{50} +(1.37541 + 1.62686i) q^{52} +(2.55252 + 6.16232i) q^{53} +(-5.16815 - 5.16815i) q^{55} +(-0.736256 - 10.3507i) q^{56} +(3.50063 + 2.55680i) q^{58} +(8.95423 - 3.70896i) q^{59} +(-2.00717 + 4.84573i) q^{61} +(-0.515295 + 2.12287i) q^{62} +(-1.13236 - 7.91945i) q^{64} -1.38825 q^{65} +(1.14380 - 2.76138i) q^{67} +(0.897707 - 1.74020i) q^{68} +(5.46066 + 3.98838i) q^{70} +(-10.0373 + 10.0373i) q^{71} +(8.11103 + 8.11103i) q^{73} +(-1.94035 - 12.4531i) q^{74} +(-7.95200 - 9.40578i) q^{76} +(-19.0083 - 7.87349i) q^{77} +0.155459i q^{79} +(4.41742 + 2.76837i) q^{80} +(-1.89342 + 1.15376i) q^{82} +(-5.13862 - 2.12849i) q^{83} +(0.488304 + 1.17887i) q^{85} +(12.6745 - 1.97484i) q^{86} +(-15.0481 - 5.01498i) q^{88} +(6.15303 - 6.15303i) q^{89} +(-3.61044 + 1.49549i) q^{91} +(-3.18569 - 9.97462i) q^{92} +(4.33707 + 1.05276i) q^{94} +8.02623 q^{95} +14.3852 q^{97} +(8.87798 + 2.15499i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

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