LMFDB - Embedded newform 504.2.bk.c.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.321935 - 1.37708i) q^{2} +(-1.79272 - 0.886663i) q^{4} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(-1.79815 + 2.18327i) q^{8} +O(q^{10})$	\(q+(0.321935 - 1.37708i) q^{2} +(-1.79272 - 0.886663i) q^{4} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(-1.79815 + 2.18327i) q^{8} +(2.58215 + 2.42127i) q^{10} +(-2.83809 - 4.91572i) q^{11} -5.31228 q^{13} +(-2.68370 - 2.60725i) q^{14} +(2.42766 + 3.17907i) q^{16} +(0.393919 - 0.227429i) q^{17} +(-3.19938 - 1.84716i) q^{19} +(4.16558 - 2.77635i) q^{20} +(-7.68304 + 2.32575i) q^{22} +(-4.43443 - 2.56022i) q^{23} +(-0.632521 - 1.09556i) q^{25} +(-1.71021 + 7.31545i) q^{26} +(-4.45438 + 2.85632i) q^{28} -2.57962i q^{29} +(3.00333 + 5.20192i) q^{31} +(5.15939 - 2.31963i) q^{32} +(-0.186372 - 0.615676i) q^{34} +(3.20917 + 5.79280i) q^{35} +(-7.80778 - 4.50782i) q^{37} +(-3.57369 + 3.81115i) q^{38} +(-2.48222 - 6.63015i) q^{40} +4.65692i q^{41} +3.66703 q^{43} +(0.729306 + 11.3289i) q^{44} +(-4.95323 + 5.28235i) q^{46} +(0.478841 - 0.829377i) q^{47} +(-3.28332 - 6.18222i) q^{49} +(-1.71230 + 0.518335i) q^{50} +(9.52341 + 4.71020i) q^{52} +(5.41124 - 3.12418i) q^{53} +14.2075 q^{55} +(2.49936 + 7.05359i) q^{56} +(-3.55235 - 0.830471i) q^{58} +(8.76604 - 5.06108i) q^{59} +(-2.50184 + 4.33331i) q^{61} +(8.13036 - 2.46115i) q^{62} +(-1.53334 - 7.85168i) q^{64} +(6.64834 - 11.5153i) q^{65} +(4.65133 + 8.05634i) q^{67} +(-0.907837 + 0.0584425i) q^{68} +(9.01031 - 2.55439i) q^{70} -7.35240i q^{71} +(5.93541 - 3.42681i) q^{73} +(-8.72125 + 9.30073i) q^{74} +(4.09777 + 6.14821i) q^{76} +(-15.0154 - 0.265718i) q^{77} +(-7.71882 - 4.45646i) q^{79} +(-9.92938 + 1.28374i) q^{80} +(6.41297 + 1.49923i) q^{82} +1.96259i q^{83} +1.13851i q^{85} +(1.18055 - 5.04980i) q^{86} +(15.8357 + 2.64286i) q^{88} +(-5.91361 - 3.41423i) q^{89} +(-7.24175 + 12.0457i) q^{91} +(5.67961 + 8.52158i) q^{92} +(-0.987965 - 0.926409i) q^{94} +(8.00807 - 4.62346i) q^{95} -3.71270i q^{97} +(-9.57044 + 2.53113i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.321935	−	1.37708i	0.227643	−	0.973745i
$2$	0.321935	−	1.37708i	0.227643	−	0.973745i
$3$		0			0
$3$		0			0
$4$	−1.79272	−	0.886663i	−0.896358	−	0.443331i
$5$	−1.25150	+	2.16767i	−0.559689	+	0.969410i	0.437833	+	0.899056i	$0.355746\pi$
$5$	−1.25150	+	2.16767i	−0.559689	+	0.969410i	−0.997522	+	0.0703538i	$0.977587\pi$
$6$		0			0
$7$	1.36321	−	2.26752i	0.515245	−	0.857043i
$7$	1.36321	−	2.26752i	0.515245	−	0.857043i
$8$	−1.79815	+	2.18327i	−0.635741	+	0.771903i
$9$		0			0
$10$	2.58215	+	2.42127i	0.816549	+	0.765673i
$11$	−2.83809	−	4.91572i	−0.855717	−	1.48215i	−0.875978	−	0.482351i	$-0.839783\pi$
$11$	−2.83809	−	4.91572i	−0.855717	−	1.48215i	0.0202603	−	0.999795i	$-0.493550\pi$
$12$		0			0
$13$	−5.31228			−1.47336			−0.736681	−	0.676241i	$-0.763608\pi$
$13$	−5.31228			−1.47336			−0.736681	+	0.676241i	$0.763608\pi$
$14$	−2.68370	−	2.60725i	−0.717250	−	0.696816i
$15$		0			0
$16$	2.42766	+	3.17907i	0.606914	+	0.794767i
$17$	0.393919	−	0.227429i	0.0955393	−	0.0551596i	−0.451469	−	0.892287i	$-0.649100\pi$
$17$	0.393919	−	0.227429i	0.0955393	−	0.0551596i	0.547008	+	0.837127i	$0.315767\pi$
$18$		0			0
$19$	−3.19938	−	1.84716i	−0.733988	−	0.423768i	0.0858912	−	0.996305i	$-0.472626\pi$
$19$	−3.19938	−	1.84716i	−0.733988	−	0.423768i	−0.819879	+	0.572536i	$0.805960\pi$
$20$	4.16558	−	2.77635i	0.931452	−	0.620811i
$21$		0			0
$22$	−7.68304	+	2.32575i	−1.63803	+	0.495851i
$23$	−4.43443	−	2.56022i	−0.924642	−	0.533842i	−0.0395287	−	0.999218i	$-0.512586\pi$
$23$	−4.43443	−	2.56022i	−0.924642	−	0.533842i	−0.885113	+	0.465376i	$0.845919\pi$
$24$		0			0
$25$	−0.632521	−	1.09556i	−0.126504	−	0.219112i
$26$	−1.71021	+	7.31545i	−0.335400	+	1.43468i
$27$		0			0
$28$	−4.45438	+	2.85632i	−0.841798	+	0.539793i
$29$		−	2.57962i		−	0.479024i	−0.970893	−	0.239512i	$-0.923013\pi$
$29$		−	2.57962i		−	0.479024i	0.970893	−	0.239512i	$-0.0769874\pi$
$30$		0			0
$31$	3.00333	+	5.20192i	0.539414	+	0.934293i	0.998936	+	0.0461260i	$0.0146876\pi$
$31$	3.00333	+	5.20192i	0.539414	+	0.934293i	−0.459521	+	0.888167i	$0.651979\pi$
$32$	5.15939	−	2.31963i	0.912060	−	0.410057i
$33$		0			0
$34$	−0.186372	−	0.615676i	−0.0319626	−	0.105588i
$35$	3.20917	+	5.79280i	0.542449	+	0.979161i
$36$		0			0
$37$	−7.80778	−	4.50782i	−1.28359	−	0.741082i	−0.306088	−	0.952003i	$-0.599020\pi$
$37$	−7.80778	−	4.50782i	−1.28359	−	0.741082i	−0.977503	+	0.210922i	$0.932354\pi$
$38$	−3.57369	+	3.81115i	−0.579729	+	0.618250i
$39$		0			0
$40$	−2.48222	−	6.63015i	−0.392473	−	1.04832i
$41$			4.65692i			0.727289i	0.931538	+	0.363644i	$0.118468\pi$
$41$			4.65692i			0.727289i	−0.931538	+	0.363644i	$0.881532\pi$
$42$		0			0
$43$	3.66703			0.559217			0.279608	−	0.960114i	$-0.409795\pi$
$43$	3.66703			0.559217			0.279608	+	0.960114i	$0.409795\pi$
$44$	0.729306	+	11.3289i	0.109947	+	1.70790i
$45$		0			0
$46$	−4.95323	+	5.28235i	−0.730314	+	0.778840i
$47$	0.478841	−	0.829377i	0.0698461	−	0.120977i	−0.828987	−	0.559267i	$-0.811082\pi$
$47$	0.478841	−	0.829377i	0.0698461	−	0.120977i	0.898833	+	0.438290i	$0.144416\pi$
$48$		0			0
$49$	−3.28332	−	6.18222i	−0.469046	−	0.883174i
$50$	−1.71230	+	0.518335i	−0.242156	+	0.0733036i
$51$		0			0
$52$	9.52341	+	4.71020i	1.32066	+	0.653188i
$53$	5.41124	−	3.12418i	0.743290	−	0.429139i	−0.0799741	−	0.996797i	$-0.525484\pi$
$53$	5.41124	−	3.12418i	0.743290	−	0.429139i	0.823264	+	0.567658i	$0.192150\pi$
$54$		0			0
$55$	14.2075			1.91574
$56$	2.49936	+	7.05359i	0.333992	+	0.942576i
$57$		0			0
$58$	−3.55235	−	0.830471i	−0.466447	−	0.109046i
$59$	8.76604	−	5.06108i	1.14124	−	0.658896i	0.194503	−	0.980902i	$-0.437690\pi$
$59$	8.76604	−	5.06108i	1.14124	−	0.658896i	0.946738	+	0.322006i	$0.104357\pi$
$60$		0			0
$61$	−2.50184	+	4.33331i	−0.320327	+	0.554823i	−0.980555	−	0.196242i	$-0.937126\pi$
$61$	−2.50184	+	4.33331i	−0.320327	+	0.554823i	0.660228	+	0.751065i	$0.270460\pi$
$62$	8.13036	−	2.46115i	1.03256	−	0.312567i
$63$		0			0
$64$	−1.53334	−	7.85168i	−0.191667	−	0.981460i
$65$	6.64834	−	11.5153i	0.824625	−	1.42829i
$66$		0			0
$67$	4.65133	+	8.05634i	0.568251	+	0.984239i	0.996739	+	0.0806916i	$0.0257129\pi$
$67$	4.65133	+	8.05634i	0.568251	+	0.984239i	−0.428489	+	0.903547i	$0.640954\pi$
$68$	−0.907837	+	0.0584425i	−0.110091	+	0.00708720i
$69$		0			0
$70$	9.01031	−	2.55439i	1.07694	−	0.305308i
$71$		−	7.35240i		−	0.872569i	−0.899809	−	0.436285i	$-0.856294\pi$
$71$		−	7.35240i		−	0.872569i	0.899809	−	0.436285i	$-0.143706\pi$
$72$		0			0
$73$	5.93541	−	3.42681i	0.694687	−	0.401078i	−0.110678	−	0.993856i	$-0.535302\pi$
$73$	5.93541	−	3.42681i	0.694687	−	0.401078i	0.805366	+	0.592779i	$0.201969\pi$
$74$	−8.72125	+	9.30073i	−1.01382	+	1.08119i
$75$		0			0
$76$	4.09777	+	6.14821i	0.470046	+	0.705248i
$77$	−15.0154	−	0.265718i	−1.71117	−	0.0302814i
$78$		0			0
$79$	−7.71882	−	4.45646i	−0.868435	−	0.501391i	−0.00160740	−	0.999999i	$-0.500512\pi$
$79$	−7.71882	−	4.45646i	−0.868435	−	0.501391i	−0.866828	+	0.498607i	$0.833845\pi$
$80$	−9.92938	+	1.28374i	−1.11014	+	0.143526i
$81$		0			0
$82$	6.41297	+	1.49923i	0.708194	+	0.165562i
$83$			1.96259i			0.215423i	0.994182	+	0.107711i	$0.0343522\pi$
$83$			1.96259i			0.215423i	−0.994182	+	0.107711i	$0.965648\pi$
$84$		0			0
$85$			1.13851i			0.123489i
$86$	1.18055	−	5.04980i	0.127302	−	0.544534i
$87$		0			0
$88$	15.8357	+	2.64286i	1.68809	+	0.281730i
$89$	−5.91361	−	3.41423i	−0.626842	−	0.361907i	0.152686	−	0.988275i	$-0.451208\pi$
$89$	−5.91361	−	3.41423i	−0.626842	−	0.361907i	−0.779528	+	0.626367i	$0.784541\pi$
$90$		0			0
$91$	−7.24175	+	12.0457i	−0.759142	+	1.26273i
$92$	5.67961	+	8.52158i	0.592141	+	0.888436i
$93$		0			0
$94$	−0.987965	−	0.926409i	−0.101901	−	0.0955518i
$95$	8.00807	−	4.62346i	0.821611	−	0.474357i
$96$		0			0
$97$		−	3.71270i		−	0.376967i	−0.982076	−	0.188484i	$-0.939643\pi$
$97$		−	3.71270i		−	0.376967i	0.982076	−	0.188484i	$-0.0603573\pi$
$98$	−9.57044	+	2.53113i	−0.966761	+	0.255683i
$99$		0			0
$100$	0.162539	+	2.52486i	0.0162539	+	0.252486i
$101$	−2.84077	−	4.92036i	−0.282667	−	0.489594i	0.689373	−	0.724406i	$-0.257886\pi$
$101$	−2.84077	−	4.92036i	−0.282667	−	0.489594i	−0.972041	+	0.234812i	$0.924553\pi$
$102$		0			0
$103$	2.95345	−	5.11553i	0.291013	−	0.504049i	−0.683037	−	0.730384i	$-0.739341\pi$
$103$	2.95345	−	5.11553i	0.291013	−	0.504049i	0.974049	+	0.226335i	$0.0726745\pi$
$104$	9.55226	−	11.5981i	0.936676	−	1.13729i
$105$		0			0
$106$	−2.56019	−	8.45750i	−0.248667	−	0.821465i
$107$	−5.33045	+	9.23261i	−0.515314	+	0.892550i	0.484528	+	0.874776i	$0.338991\pi$
$107$	−5.33045	+	9.23261i	−0.515314	+	0.892550i	−0.999842	+	0.0177741i	$0.994342\pi$
$108$		0			0
$109$	2.75319	−	1.58956i	0.263708	−	0.152252i	−0.362317	−	0.932055i	$-0.618014\pi$
$109$	2.75319	−	1.58956i	0.263708	−	0.152252i	0.626025	+	0.779803i	$0.284681\pi$
$110$	4.57390	−	19.5650i	0.436105	−	1.86545i
$111$		0			0
$112$	10.5180	−	1.17103i	0.993859	−	0.110652i
$113$	0.302446			0.0284518			0.0142259	−	0.999899i	$-0.495472\pi$
$113$	0.302446			0.0284518			0.0142259	+	0.999899i	$0.495472\pi$
$114$		0			0
$115$	11.0994	−	6.40824i	1.03502	−	0.597571i
$116$	−2.28726	+	4.62453i	−0.212366	+	0.429377i
$117$		0			0
$118$	−4.14742	−	13.7009i	−0.381801	−	1.26127i
$119$	0.0212932	−	1.20325i	0.00195194	−	0.110302i
$120$		0			0
$121$	−10.6096	+	18.3763i	−0.964505	+	1.67057i
$122$	5.16189	+	4.84028i	0.467336	+	0.438218i
$123$		0			0
$124$	−0.771767	−	11.9885i	−0.0693067	−	1.07660i
$125$	−9.34863			−0.836167
$126$		0			0
$127$		−	6.39751i		−	0.567687i	−0.958871	−	0.283843i	$-0.908390\pi$
$127$		−	6.39751i		−	0.567687i	0.958871	−	0.283843i	$-0.0916096\pi$
$128$	−11.3061	−	0.416198i	−0.999323	−	0.0367871i
$129$		0			0
$130$	−13.7171	−	12.8625i	−1.20307	−	1.12811i
$131$	12.5596	+	7.25130i	1.09734	+	0.633549i	0.935521	−	0.353272i	$-0.114931\pi$
$131$	12.5596	+	7.25130i	1.09734	+	0.633549i	0.161818	+	0.986821i	$0.448264\pi$
$132$		0			0
$133$	−8.54991	+	4.73660i	−0.741371	+	0.410715i
$134$	12.5917	−	3.81165i	1.08776	−	0.329276i
$135$		0			0
$136$	−0.211784	+	1.26898i	−0.0181604	+	0.108814i
$137$	0.615559	+	1.06618i	0.0525908	+	0.0910899i	0.891122	−	0.453763i	$-0.149919\pi$
$137$	0.615559	+	1.06618i	0.0525908	+	0.0910899i	−0.838532	+	0.544853i	$0.816585\pi$
$138$		0			0
$139$		−	15.7788i		−	1.33834i	−0.743108	−	0.669172i	$-0.766649\pi$
$139$		−	15.7788i		−	1.33834i	0.743108	−	0.669172i	$-0.233351\pi$
$140$	−0.616877	−	13.2303i	−0.0521356	−	1.11816i
$141$		0			0
$142$	−10.1249	−	2.36700i	−0.849660	−	0.198634i
$143$	15.0768	+	26.1137i	1.26078	+	2.18374i
$144$		0			0
$145$	5.59176	+	3.22841i	0.464371	+	0.268104i
$146$	−2.80819	−	9.27676i	−0.232407	−	0.767750i
$147$		0			0
$148$	10.0002	+	15.0041i	0.822012	+	1.23333i
$149$	5.15767	+	2.97778i	0.422532	+	0.243949i	0.696160	−	0.717886i	$-0.254890\pi$
$149$	5.15767	+	2.97778i	0.422532	+	0.243949i	−0.273628	+	0.961836i	$0.588224\pi$
$150$		0			0
$151$	3.11126	−	1.79629i	0.253191	−	0.146180i	−0.368034	−	0.929812i	$-0.619969\pi$
$151$	3.11126	−	1.79629i	0.253191	−	0.146180i	0.621224	+	0.783633i	$0.286636\pi$
$152$	9.78581	−	3.66364i	0.793734	−	0.297161i
$153$		0			0
$154$	−5.19991	+	20.5920i	−0.419021	+	1.65935i
$155$	−15.0347			−1.20762
$156$		0			0
$157$	−0.491762	−	0.851757i	−0.0392469	−	0.0679776i	0.845735	−	0.533604i	$-0.179163\pi$
$157$	−0.491762	−	0.851757i	−0.0392469	−	0.0679776i	−0.884982	+	0.465626i	$0.845829\pi$
$158$	−8.62188	+	9.19477i	−0.685920	+	0.731496i
$159$		0			0
$160$	−1.42880	+	14.0869i	−0.112957	+	1.11366i
$161$	−11.8504	+	6.56505i	−0.933942	+	0.517398i
$162$		0			0
$163$	−1.26083	+	2.18383i	−0.0987562	+	0.171051i	−0.911170	−	0.412030i	$-0.864820\pi$
$163$	−1.26083	+	2.18383i	−0.0987562	+	0.171051i	0.812414	+	0.583081i	$0.198153\pi$
$164$	4.12912	−	8.34854i	0.322430	−	0.651911i
$165$		0			0
$166$	2.70266	+	0.631828i	0.209767	+	0.0490394i
$167$	5.26232			0.407211			0.203605	−	0.979053i	$-0.434734\pi$
$167$	5.26232			0.407211			0.203605	+	0.979053i	$0.434734\pi$
$168$		0			0
$169$	15.2203			1.17079
$170$	1.56783	+	0.366527i	0.120247	+	0.0281114i
$171$		0			0
$172$	−6.57394	−	3.25142i	−0.501258	−	0.247918i
$173$	0.0718117	−	0.124381i	0.00545974	−	0.00945654i	−0.863283	−	0.504721i	$-0.831595\pi$
$173$	0.0718117	−	0.124381i	0.00545974	−	0.00945654i	0.868742	+	0.495264i	$0.164929\pi$
$174$		0			0
$175$	−3.34646	−	0.0592202i	−0.252969	−	0.00447662i
$176$	8.73750	−	20.9562i	0.658614	−	1.57963i
$177$		0			0
$178$	−6.60547	+	7.04438i	−0.495101	+	0.527998i
$179$	−9.46239	−	16.3893i	−0.707252	−	1.22500i	−0.965873	−	0.259018i	$-0.916601\pi$
$179$	−9.46239	−	16.3893i	−0.707252	−	1.22500i	0.258621	−	0.965979i	$-0.416732\pi$
$180$		0			0
$181$	22.2260			1.65204			0.826022	−	0.563637i	$-0.190598\pi$
$181$	22.2260			1.65204			0.826022	+	0.563637i	$0.190598\pi$
$182$	14.2566	+	13.8504i	1.05677	+	1.02666i
$183$		0			0
$184$	13.5634	−	5.07790i	0.999906	−	0.374348i
$185$	19.5429	−	11.2831i	1.43682	−	0.829551i
$186$		0			0
$187$	−2.23596	−	1.29093i	−0.163509	−	0.0944021i
$188$	−1.59380	+	1.06227i	−0.116240	+	0.0774737i
$189$		0			0
$190$	−3.78881	−	12.5162i	−0.274869	−	0.908023i
$191$	10.2112	+	5.89547i	0.738860	+	0.426581i	0.821655	−	0.569986i	$-0.193051\pi$
$191$	10.2112	+	5.89547i	0.738860	+	0.426581i	−0.0827947	+	0.996567i	$0.526385\pi$
$192$		0			0
$193$	−13.4112	−	23.2289i	−0.965361	−	1.67205i	−0.708642	−	0.705568i	$-0.750692\pi$
$193$	−13.4112	−	23.2289i	−0.965361	−	1.67205i	−0.256719	−	0.966486i	$-0.582641\pi$
$194$	−5.11270	−	1.19525i	−0.367070	−	0.0858138i
$195$		0			0
$196$	0.404513	+	13.9942i	0.0288938	+	0.999582i
$197$			16.5842i			1.18157i	0.806828	+	0.590786i	$0.201182\pi$
$197$			16.5842i			1.18157i	−0.806828	+	0.590786i	$0.798818\pi$
$198$		0			0
$199$	5.70420	+	9.87996i	0.404360	+	0.700372i	0.994247	−	0.107114i	$-0.0341610\pi$
$199$	5.70420	+	9.87996i	0.404360	+	0.700372i	−0.589887	+	0.807486i	$0.700828\pi$
$200$	3.52926	+	0.589010i	0.249557	+	0.0416493i
$201$		0			0
$202$	−7.69029	+	2.32794i	−0.541087	+	0.163793i
$203$	−5.84935	−	3.51657i	−0.410544	−	0.246815i
$204$		0			0
$205$	−10.0947	−	5.82815i	−0.705041	−	0.407056i
$206$	−6.09369	−	5.71402i	−0.424568	−	0.398115i
$207$		0			0
$208$	−12.8964	−	16.8881i	−0.894205	−	1.17098i
$209$			20.9697i			1.45050i
$210$		0			0
$211$	−4.13300			−0.284527			−0.142264	−	0.989829i	$-0.545438\pi$
$211$	−4.13300			−0.284527			−0.142264	+	0.989829i	$0.545438\pi$
$212$	−12.4709	+	0.802821i	−0.856505	+	0.0551380i
$213$		0			0
$214$	10.9980	+	10.3128i	0.751808	+	0.704966i
$215$	−4.58930	+	7.94890i	−0.312988	+	0.542110i
$216$		0			0
$217$	15.8896	+	0.281189i	1.07866	+	0.0190883i
$218$	−1.30260	−	4.30311i	−0.0882233	−	0.291443i
$219$		0			0
$220$	−25.4701	−	12.5973i	−1.71719	−	0.849309i
$221$	−2.09261	+	1.20817i	−0.140764	+	0.0812701i
$222$		0			0
$223$	−18.1063			−1.21249			−0.606245	−	0.795278i	$-0.707325\pi$
$223$	−18.1063			−1.21249			−0.606245	+	0.795278i	$0.707325\pi$
$224$	1.77351	−	14.8612i	0.118498	−	0.992954i
$225$		0			0
$226$	0.0973682	−	0.416494i	0.00647683	−	0.0277048i
$227$	−6.86343	+	3.96260i	−0.455542	+	0.263007i	−0.710168	−	0.704032i	$-0.751381\pi$
$227$	−6.86343	+	3.96260i	−0.455542	+	0.263007i	0.254626	+	0.967040i	$0.418048\pi$
$228$		0			0
$229$	1.07787	−	1.86692i	0.0712274	−	0.123370i	−0.828212	−	0.560415i	$-0.810642\pi$
$229$	1.07787	−	1.86692i	0.0712274	−	0.123370i	0.899440	+	0.437045i	$0.143975\pi$
$230$	−5.25139	−	17.3478i	−0.346266	−	1.14388i
$231$		0			0
$232$	5.63201	+	4.63854i	0.369760	+	0.304535i
$233$	−10.0072	+	17.3330i	−0.655594	+	1.13552i	0.326151	+	0.945318i	$0.394248\pi$
$233$	−10.0072	+	17.3330i	−0.655594	+	1.13552i	−0.981745	+	0.190204i	$0.939085\pi$
$234$		0			0
$235$	1.19854	+	2.07594i	0.0781843	+	0.135419i
$236$	−20.2025	+	1.30055i	−1.31507	+	0.0846583i
$237$		0			0
$238$	−1.65012	−	0.416692i	−0.106962	−	0.0270101i
$239$		−	18.8923i		−	1.22204i	−0.791614	−	0.611021i	$-0.790759\pi$
$239$		−	18.8923i		−	1.22204i	0.791614	−	0.611021i	$-0.209241\pi$
$240$		0			0
$241$	−15.8555	+	9.15417i	−1.02134	+	0.589672i	−0.914492	−	0.404603i	$-0.867410\pi$
$241$	−15.8555	+	9.15417i	−1.02134	+	0.589672i	−0.106849	+	0.994275i	$0.534076\pi$
$242$	21.8901	+	20.5262i	1.40715	+	1.31947i
$243$		0			0
$244$	8.32726	−	5.55010i	0.533098	−	0.355309i
$245$	17.5101	+	0.619923i	1.11868	+	0.0396054i
$246$		0			0
$247$	16.9960	+	9.81265i	1.08143	+	0.624364i
$248$	−16.7576	−	2.79673i	−1.06411	−	0.177593i
$249$		0			0
$250$	−3.00965	+	12.8738i	−0.190347	+	0.814213i
$251$			3.43251i			0.216658i	0.994115	+	0.108329i	$0.0345500\pi$
$251$			3.43251i			0.216658i	−0.994115	+	0.108329i	$0.965450\pi$
$252$		0			0
$253$			29.0645i			1.82727i
$254$	−8.80990	−	2.05958i	−0.552782	−	0.129230i
$255$		0			0
$256$	−4.21295	+	15.4354i	−0.263310	+	0.964711i
$257$	−21.7104	−	12.5345i	−1.35426	−	0.781882i	−0.365417	−	0.930844i	$-0.619073\pi$
$257$	−21.7104	−	12.5345i	−1.35426	−	0.781882i	−0.988843	+	0.148962i	$0.952407\pi$
$258$		0			0
$259$	−20.8652	+	11.5592i	−1.29650	+	0.718254i
$260$	−22.1287	+	14.7487i	−1.37237	+	0.914678i
$261$		0			0
$262$	14.0290	−	14.9612i	0.866716	−	0.924305i
$263$	−13.4314	+	7.75460i	−0.828214	+	0.478169i	−0.853241	−	0.521517i	$-0.825366\pi$
$263$	−13.4314	+	7.75460i	−0.828214	+	0.478169i	0.0250270	+	0.999687i	$0.492033\pi$
$264$		0			0
$265$			15.6397i			0.960738i
$266$	3.77017	+	13.2988i	0.231164	+	0.815403i
$267$		0			0
$268$	−1.19525	−	18.5669i	−0.0730118	−	1.13415i
$269$	11.8667	+	20.5537i	0.723523	+	1.25318i	0.959579	+	0.281440i	$0.0908120\pi$
$269$	11.8667	+	20.5537i	0.723523	+	1.25318i	−0.236055	+	0.971740i	$0.575855\pi$
$270$		0			0
$271$	7.35684	−	12.7424i	0.446896	−	0.774047i	−0.551286	−	0.834316i	$-0.685863\pi$
$271$	7.35684	−	12.7424i	0.446896	−	0.774047i	0.998182	+	0.0602693i	$0.0191959\pi$
$272$	1.67931	+	0.700175i	0.101823	+	0.0424543i
$273$		0			0
$274$	1.66639	−	0.504436i	0.100670	−	0.0304741i
$275$	−3.59031	+	6.21859i	−0.216504	+	0.374995i
$276$		0			0
$277$	6.16822	−	3.56123i	0.370613	−	0.213973i	−0.303113	−	0.952954i	$-0.598026\pi$
$277$	6.16822	−	3.56123i	0.370613	−	0.213973i	0.673726	+	0.738981i	$0.264693\pi$
$278$	−21.7288	−	5.07976i	−1.30321	−	0.304664i
$279$		0			0
$280$	−18.4178	−	3.40981i	−1.10067	−	0.203775i
$281$	13.0561			0.778861			0.389430	−	0.921056i	$-0.372672\pi$
$281$	13.0561			0.778861			0.389430	+	0.921056i	$0.372672\pi$
$282$		0			0
$283$	−1.83051	+	1.05685i	−0.108813	+	0.0628230i	−0.553419	−	0.832903i	$-0.686677\pi$
$283$	−1.83051	+	1.05685i	−0.108813	+	0.0628230i	0.444606	+	0.895726i	$0.353344\pi$
$284$	−6.51910	+	13.1808i	−0.386837	+	0.782134i
$285$		0			0
$286$	40.8145	−	12.3550i	2.41341	−	0.730568i
$287$	10.5597	+	6.34836i	0.623318	+	0.374732i
$288$		0			0
$289$	−8.39655	+	14.5433i	−0.493915	+	0.855486i
$290$	6.24597	−	6.66098i	0.366776	−	0.391146i
$291$		0			0
$292$	−13.6789	+	0.880589i	−0.800498	+	0.0515325i
$293$	−0.334002			−0.0195126			−0.00975630	−	0.999952i	$-0.503106\pi$
$293$	−0.334002			−0.0195126			−0.00975630	+	0.999952i	$0.503106\pi$
$294$		0			0
$295$			25.3358i			1.47511i
$296$	23.8813	−	8.94077i	1.38807	−	0.519671i
$297$		0			0
$298$	5.76108	−	6.14388i	0.333731	−	0.355906i
$299$	23.5569	+	13.6006i	1.36233	+	0.786542i
$300$		0			0
$301$	4.99893	−	8.31507i	0.288134	−	0.479273i
$302$	−1.47201	−	4.86275i	−0.0847047	−	0.279820i
$303$		0			0
$304$	−1.89474	−	14.6553i	−0.108671	−	0.840541i
$305$	−6.26211	−	10.8463i	−0.358567	−	0.621057i
$306$		0			0
$307$			9.39141i			0.535996i	0.963419	+	0.267998i	$0.0863621\pi$
$307$			9.39141i			0.535996i	−0.963419	+	0.267998i	$0.913638\pi$
$308$	26.6828	+	13.7900i	1.52039	+	0.785757i
$309$		0			0
$310$	−4.84020	+	20.7040i	−0.274905	+	1.17591i
$311$	−7.93750	−	13.7482i	−0.450095	−	0.779587i	0.548297	−	0.836284i	$-0.315276\pi$
$311$	−7.93750	−	13.7482i	−0.450095	−	0.779587i	−0.998391	+	0.0566971i	$0.981943\pi$
$312$		0			0
$313$	−27.8562	−	16.0828i	−1.57453	−	0.909054i	−0.995603	−	0.0936727i	$-0.970139\pi$
$313$	−27.8562	−	16.0828i	−1.57453	−	0.909054i	−0.578924	−	0.815381i	$-0.696527\pi$
$314$	−1.33125	+	0.402987i	−0.0751271	+	0.0227418i
$315$		0			0
$316$	9.88627	+	14.8332i	0.556146	+	0.834431i
$317$	−13.2252	−	7.63558i	−0.742802	−	0.428857i	0.0802854	−	0.996772i	$-0.474417\pi$
$317$	−13.2252	−	7.63558i	−0.742802	−	0.428857i	−0.823087	+	0.567915i	$0.807750\pi$
$318$		0			0
$319$	−12.6807	+	7.32121i	−0.709983	+	0.409909i
$320$	18.9388	+	6.50264i	1.05871	+	0.363508i
$321$		0			0
$322$	5.22556	+	18.4325i	0.291209	+	1.02720i
$323$	−1.68039			−0.0934996
$324$		0			0
$325$	3.36013	+	5.81991i	0.186386	+	0.322831i
$326$	2.60141	+	2.43933i	0.144079	+	0.135102i
$327$		0			0
$328$	−10.1673	−	8.37383i	−0.561396	−	0.462367i
$329$	−1.22787	−	2.21640i	−0.0676947	−	0.122194i
$330$		0			0
$331$	10.5189	−	18.2193i	0.578174	−	1.00143i	−0.417515	−	0.908670i	$-0.637099\pi$
$331$	10.5189	−	18.2193i	0.578174	−	1.00143i	0.995689	−	0.0927561i	$-0.0295677\pi$
$332$	1.74016	−	3.51837i	0.0955037	−	0.193096i
$333$		0			0
$334$	1.69413	−	7.24665i	0.0926984	−	0.396519i
$335$	−23.2846			−1.27217
$336$		0			0
$337$	1.18351			0.0644697			0.0322348	−	0.999480i	$-0.489738\pi$
$337$	1.18351			0.0644697			0.0322348	+	0.999480i	$0.489738\pi$
$338$	4.89996	−	20.9597i	0.266523	−	1.14006i
$339$		0			0
$340$	1.00948	−	2.04103i	0.0547466	−	0.110690i
$341$	17.0475	−	29.5271i	0.923172	−	1.59898i
$342$		0			0
$343$	−18.4942	−	0.982659i	−0.998591	−	0.0530586i
$344$	−6.59386	+	8.00612i	−0.355517	+	0.431661i
$345$		0			0
$346$	−0.148165	−	0.138933i	−0.00796539	−	0.00746910i
$347$	−2.40670	−	4.16854i	−0.129199	−	0.223779i	0.794168	−	0.607699i	$-0.207907\pi$
$347$	−2.40670	−	4.16854i	−0.129199	−	0.223779i	−0.923366	+	0.383920i	$0.874574\pi$
$348$		0			0
$349$	−35.4792			−1.89916			−0.949578	−	0.313530i	$-0.898488\pi$
$349$	−35.4792			−1.89916			−0.949578	+	0.313530i	$0.898488\pi$
$350$	−1.15889	+	4.58929i	−0.0619455	+	0.245308i
$351$		0			0
$352$	−26.0455	−	18.7788i	−1.38823	−	1.00091i
$353$	4.13712	−	2.38857i	0.220197	−	0.127131i	−0.385845	−	0.922564i	$-0.626090\pi$
$353$	4.13712	−	2.38857i	0.220197	−	0.127131i	0.606041	+	0.795433i	$0.292757\pi$
$354$		0			0
$355$	15.9375	+	9.20155i	0.845877	+	0.488367i
$356$	7.57416	+	11.3641i	0.401430	+	0.602297i
$357$		0			0
$358$	−25.6158	+	7.75419i	−1.35383	+	0.409822i
$359$	−31.9690	−	18.4573i	−1.68726	−	0.974140i	−0.956603	−	0.291394i	$-0.905881\pi$
$359$	−31.9690	−	18.4573i	−1.68726	−	0.974140i	−0.730656	−	0.682745i	$-0.760786\pi$
$360$		0			0
$361$	−2.67598	−	4.63493i	−0.140841	−	0.243943i
$362$	7.15533	−	30.6070i	0.376076	−	1.60867i
$363$		0			0
$364$	23.6629	−	15.1736i	1.24027	−	0.795310i
$365$			17.1547i			0.897916i
$366$		0			0
$367$	0.284416	+	0.492623i	0.0148464	+	0.0257147i	0.873353	−	0.487088i	$-0.161941\pi$
$367$	0.284416	+	0.492623i	0.0148464	+	0.0257147i	−0.858507	+	0.512802i	$0.828607\pi$
$368$	−2.62616	−	20.3127i	−0.136898	−	1.05887i
$369$		0			0
$370$	−9.24623	−	30.5447i	−0.480689	−	1.58794i
$371$	0.292503	−	16.5290i	0.0151860	−	0.858143i
$372$		0			0
$373$	20.2929	+	11.7161i	1.05073	+	0.606638i	0.922853	−	0.385153i	$-0.125851\pi$
$373$	20.2929	+	11.7161i	1.05073	+	0.606638i	0.127874	+	0.991790i	$0.459185\pi$
$374$	−2.49755	+	2.66350i	−0.129145	+	0.137726i
$375$		0			0
$376$	0.949728	+	2.53678i	0.0489785	+	0.130824i
$377$			13.7037i			0.705775i
$378$		0			0
$379$	−14.7240			−0.756320			−0.378160	−	0.925740i	$-0.623443\pi$
$379$	−14.7240			−0.756320			−0.378160	+	0.925740i	$0.623443\pi$
$380$	−18.4556	+	1.18809i	−0.946755	+	0.0609479i
$381$		0			0
$382$	11.4059	−	12.1638i	0.583577	−	0.622353i
$383$	2.49754	−	4.32587i	0.127618	−	0.221042i	−0.795135	−	0.606432i	$-0.792600\pi$
$383$	2.49754	−	4.32587i	0.127618	−	0.221042i	0.922753	+	0.385391i	$0.125933\pi$
$384$		0			0
$385$	19.3678	−	32.2159i	0.987077	−	1.64187i
$386$	−36.3057	+	10.9902i	−1.84791	+	0.559385i
$387$		0			0
$388$	−3.29191	+	6.65581i	−0.167122	+	0.337898i
$389$	27.6098	−	15.9405i	1.39987	−	0.808216i	0.405492	−	0.914099i	$-0.367100\pi$
$389$	27.6098	−	15.9405i	1.39987	−	0.808216i	0.994379	+	0.105883i	$0.0337668\pi$
$390$		0			0
$391$	−2.32907			−0.117786
$392$	19.4013	+	3.94816i	0.979916	+	0.199412i
$393$		0			0
$394$	22.8378	+	5.33902i	1.15055	+	0.268976i
$395$	19.3203	−	11.1546i	0.972108	−	0.561247i
$396$		0			0
$397$	16.4530	−	28.4975i	0.825753	−	1.43025i	−0.0755896	−	0.997139i	$-0.524084\pi$
$397$	16.4530	−	28.4975i	0.825753	−	1.43025i	0.901343	−	0.433107i	$-0.142583\pi$
$398$	15.4419	−	4.67445i	0.774033	−	0.234309i
$399$		0			0
$400$	1.94731	−	4.67047i	0.0973655	−	0.233523i
$401$	0.106236	−	0.184006i	0.00530517	−	0.00918883i	−0.863361	−	0.504587i	$-0.831645\pi$
$401$	0.106236	−	0.184006i	0.00530517	−	0.00918883i	0.868666	+	0.495399i	$0.164978\pi$
$402$		0			0
$403$	−15.9545	−	27.6341i	−0.794752	−	1.37655i
$404$	0.729994	+	11.3396i	0.0363186	+	0.564167i
$405$		0			0
$406$	−6.72571	+	6.92294i	−0.333792	+	0.343580i
$407$			51.1745i			2.53663i
$408$		0			0
$409$	17.7288	−	10.2357i	0.876633	−	0.506124i	0.00708628	−	0.999975i	$-0.497744\pi$
$409$	17.7288	−	10.2357i	0.876633	−	0.506124i	0.869547	+	0.493851i	$0.164411\pi$
$410$	−11.2757	+	12.0249i	−0.556866	+	0.593867i
$411$		0			0
$412$	−9.83046	+	6.55198i	−0.484312	+	0.322793i
$413$	0.473847	−	26.7765i	0.0233165	−	1.31759i
$414$		0			0
$415$	−4.25425	−	2.45619i	−0.208833	−	0.120570i
$416$	−27.4081	+	12.3225i	−1.34379	+	0.604162i
$417$		0			0
$418$	28.8770	+	6.75088i	1.41242	+	0.330196i
$419$		−	11.8439i		−	0.578614i	−0.957236	−	0.289307i	$-0.906575\pi$
$419$		−	11.8439i		−	0.578614i	0.957236	−	0.289307i	$-0.0934248\pi$
$420$		0			0
$421$		−	21.7928i		−	1.06211i	−0.847336	−	0.531057i	$-0.821795\pi$
$421$		−	21.7928i		−	1.06211i	0.847336	−	0.531057i	$-0.178205\pi$
$422$	−1.33056	+	5.69148i	−0.0647705	+	0.277057i
$423$		0			0
$424$	−2.90927	+	17.4319i	−0.141287	+	0.846569i
$425$	−0.498323	−	0.287707i	−0.0241722	−	0.0139558i
$426$		0			0
$427$	6.41534	+	11.5802i	0.310460	+	0.560404i
$428$	17.7422	−	11.8251i	0.857601	−	0.571589i
$429$		0			0
$430$	9.46884	+	8.87888i	0.456628	+	0.428177i
$431$	14.3234	−	8.26964i	0.689936	−	0.398335i	−0.113652	−	0.993521i	$-0.536255\pi$
$431$	14.3234	−	8.26964i	0.689936	−	0.398335i	0.803588	+	0.595186i	$0.202922\pi$
$432$		0			0
$433$			39.2724i			1.88731i	0.330929	+	0.943656i	$0.392638\pi$
$433$			39.2724i			1.88731i	−0.330929	+	0.943656i	$0.607362\pi$
$434$	5.50266	−	21.7908i	0.264136	−	1.04599i
$435$		0			0
$436$	−6.34509	+	0.408469i	−0.303875	+	0.0195621i
$437$	9.45828	+	16.3822i	0.452451	+	0.783668i
$438$		0			0
$439$	−15.5165	+	26.8754i	−0.740564	+	1.28269i	0.211674	+	0.977340i	$0.432108\pi$
$439$	−15.5165	+	26.8754i	−0.740564	+	1.28269i	−0.952239	+	0.305355i	$0.901225\pi$
$440$	−25.5472	+	31.0189i	−1.21792	+	1.47877i
$441$		0			0
$442$	0.990063	+	3.27064i	0.0470925	+	0.155569i
$443$	−0.422464	+	0.731729i	−0.0200719	+	0.0347655i	−0.875887	−	0.482517i	$-0.839723\pi$
$443$	−0.422464	+	0.731729i	−0.0200719	+	0.0347655i	0.855815	+	0.517282i	$0.173056\pi$
$444$		0			0
$445$	14.8018	−	8.54583i	0.701673	−	0.405111i
$446$	−5.82906	+	24.9339i	−0.276014	+	1.18066i
$447$		0			0
$448$	−19.8941	−	7.22661i	−0.939909	−	0.341425i
$449$	41.7433			1.96999			0.984995	−	0.172585i	$-0.0552119\pi$
$449$	41.7433			1.96999			0.984995	+	0.172585i	$0.0552119\pi$
$450$		0			0
$451$	22.8921	−	13.2168i	1.07795	−	0.622354i
$452$	−0.542201	−	0.268168i	−0.0255030	−	0.0126136i
$453$		0			0
$454$	3.24726	+	10.7272i	0.152401	+	0.503453i
$455$	−17.0480	−	30.7730i	−0.799224	−	1.44266i
$456$		0			0
$457$	3.74286	−	6.48282i	0.175083	−	0.303254i	−0.765107	−	0.643904i	$-0.777314\pi$
$457$	3.74286	−	6.48282i	0.175083	−	0.303254i	0.940190	+	0.340650i	$0.110647\pi$
$458$	−2.22390	−	2.08534i	−0.103916	−	0.0974415i
$459$		0			0
$460$	−25.5800	+	1.64673i	−1.19267	+	0.0767791i
$461$	−4.33499			−0.201901			−0.100950	−	0.994891i	$-0.532188\pi$
$461$	−4.33499			−0.201901			−0.100950	+	0.994891i	$0.532188\pi$
$462$		0			0
$463$		−	35.3200i		−	1.64146i	−0.571316	−	0.820730i	$-0.693567\pi$
$463$		−	35.3200i		−	1.64146i	0.571316	−	0.820730i	$-0.306433\pi$
$464$	8.20080	−	6.26244i	0.380712	−	0.290726i
$465$		0			0
$466$	20.6473	+	19.3609i	0.956467	+	0.896874i
$467$	−9.09213	−	5.24934i	−0.420733	−	0.242911i	0.274658	−	0.961542i	$-0.411435\pi$
$467$	−9.09213	−	5.24934i	−0.420733	−	0.242911i	−0.695391	+	0.718632i	$0.744769\pi$
$468$		0			0
$469$	24.6087	+	0.435484i	1.13632	+	0.0201088i
$470$	3.24459	−	0.982175i	0.149662	−	0.0453044i
$471$		0			0
$472$	−4.71293	+	28.2392i	−0.216930	+	1.29981i
$473$	−10.4074	−	18.0261i	−0.478532	−	0.828841i
$474$		0			0
$475$			4.67348i			0.214434i
$476$	−1.10505	+	2.13821i	−0.0506500	+	0.0980047i
$477$		0			0
$478$	−26.0163	−	6.08210i	−1.18996	−	0.278189i
$479$	−8.46375	−	14.6596i	−0.386719	−	0.669816i	0.605287	−	0.796007i	$-0.293058\pi$
$479$	−8.46375	−	14.6596i	−0.386719	−	0.669816i	−0.992006	+	0.126191i	$0.959725\pi$
$480$		0			0
$481$	41.4771	+	23.9468i	1.89119	+	1.09188i
$482$	7.50161	+	24.7814i	0.341689	+	1.12876i
$483$		0			0
$484$	35.3135	−	23.5364i	1.60516	−	1.06983i
$485$	8.04790	+	4.64645i	0.365436	+	0.210985i
$486$		0			0
$487$	20.5482	−	11.8635i	0.931127	−	0.537586i	0.0439591	−	0.999033i	$-0.486003\pi$
$487$	20.5482	−	11.8635i	0.931127	−	0.537586i	0.887168	+	0.461447i	$0.152670\pi$
$488$	−4.96211	−	13.2541i	−0.224624	−	0.599985i
$489$		0			0
$490$	6.49079	−	23.9133i	0.293224	−	1.08029i
$491$	3.41198			0.153980			0.0769901	−	0.997032i	$-0.475469\pi$
$491$	3.41198			0.153980			0.0769901	+	0.997032i	$0.475469\pi$
$492$		0			0
$493$	−0.586681	−	1.01616i	−0.0264228	−	0.0457656i
$494$	18.9844	−	20.2459i	0.854151	−	0.910905i
$495$		0			0
$496$	−9.24621	+	22.1763i	−0.415167	+	0.995744i
$497$	−16.6717	−	10.0229i	−0.747829	−	0.449587i
$498$		0			0
$499$	8.72998	−	15.1208i	0.390808	−	0.676899i	−0.601749	−	0.798686i	$-0.705529\pi$
$499$	8.72998	−	15.1208i	0.390808	−	0.676899i	0.992556	+	0.121787i	$0.0388624\pi$
$500$	16.7594	+	8.28908i	0.749504	+	0.370699i
$501$		0			0
$502$	4.72685	+	1.10505i	0.210970	+	0.0493206i
$503$	−7.08646			−0.315970			−0.157985	−	0.987442i	$-0.550500\pi$
$503$	−7.08646			−0.315970			−0.157985	+	0.987442i	$0.550500\pi$
$504$		0			0
$505$	14.2209			0.632824
$506$	40.0243	+	9.35690i	1.77930	+	0.415965i
$507$		0			0
$508$	−5.67243	+	11.4689i	−0.251673	+	0.508851i
$509$	−18.9653	+	32.8488i	−0.840622	+	1.45600i	0.0487485	+	0.998811i	$0.484477\pi$
$509$	−18.9653	+	32.8488i	−0.840622	+	1.45600i	−0.889370	+	0.457188i	$0.848857\pi$
$510$		0			0
$511$	0.320837	−	18.1301i	0.0141930	−	0.802030i
$512$	19.8995	+	10.7708i	0.879442	+	0.476006i
$513$		0			0
$514$	−24.2504	+	25.8618i	−1.06964	+	1.14071i
$515$	7.39252	+	12.8042i	0.325753	+	0.564221i
$516$		0			0
$517$	−5.43598			−0.239074
$518$	9.20074	+	32.4545i	0.404257	+	1.42597i
$519$		0			0
$520$	13.1862	+	35.2212i	0.578255	+	1.54455i
$521$	−6.91166	+	3.99045i	−0.302805	+	0.174825i	−0.643702	−	0.765276i	$-0.722603\pi$
$521$	−6.91166	+	3.99045i	−0.302805	+	0.174825i	0.340897	+	0.940101i	$0.389269\pi$
$522$		0			0
$523$	12.3267	+	7.11681i	0.539008	+	0.311196i	0.744677	−	0.667425i	$-0.232604\pi$
$523$	12.3267	+	7.11681i	0.539008	+	0.311196i	−0.205669	+	0.978622i	$0.565937\pi$
$524$	−16.0864	−	24.1357i	−0.702736	−	1.05437i
$525$		0			0
$526$	6.35470	+	20.9926i	0.277078	+	0.915320i
$527$	2.36614	+	1.36609i	0.103071	+	0.0595078i
$528$		0			0
$529$	1.60942	+	2.78759i	0.0699747	+	0.121200i
$530$	21.5371	+	5.03496i	0.935513	+	0.218705i
$531$		0			0
$532$	19.5273	−	0.910483i	0.846617	−	0.0394744i
$533$		−	24.7389i		−	1.07156i
$534$		0			0
$535$	−13.3421	−	23.1093i	−0.576831	−	0.999101i
$536$	−25.9529	−	4.33137i	−1.12100	−	0.187087i
$537$		0			0
$538$	32.1244	−	9.72444i	1.38498	−	0.419250i
$539$	−21.0717	+	33.6856i	−0.907622	+	1.45094i
$540$		0			0
$541$	−6.43282	−	3.71399i	−0.276569	−	0.159677i	0.355300	−	0.934752i	$-0.384379\pi$
$541$	−6.43282	−	3.71399i	−0.276569	−	0.159677i	−0.631869	+	0.775075i	$0.717712\pi$
$542$	−15.1790	−	14.2332i	−0.651992	−	0.611369i
$543$		0			0
$544$	1.50483	−	2.08714i	0.0645190	−	0.0894855i
$545$			7.95734i			0.340855i
$546$		0			0
$547$	−28.2287			−1.20697			−0.603485	−	0.797374i	$-0.706222\pi$
$547$	−28.2287			−1.20697			−0.603485	+	0.797374i	$0.706222\pi$
$548$	−0.158181	−	2.45715i	−0.00675714	−	0.104964i
$549$		0			0
$550$	7.40767	+	6.94613i	0.315864	+	0.296184i
$551$	−4.76498	+	8.25319i	−0.202995	+	0.351598i
$552$		0			0
$553$	−20.6275	+	11.4275i	−0.877171	+	0.485947i
$554$	−2.91834	−	9.64064i	−0.123988	−	0.409592i
$555$		0			0
$556$	−13.9905	+	28.2870i	−0.593330	+	1.19963i
$557$	−29.9378	+	17.2846i	−1.26850	+	0.732371i	−0.974705	−	0.223496i	$-0.928253\pi$
$557$	−29.9378	+	17.2846i	−1.26850	+	0.732371i	−0.293799	+	0.955867i	$0.594920\pi$
$558$		0			0
$559$	−19.4803			−0.823929
$560$	−10.6249	+	24.2651i	−0.448985	+	1.02539i
$561$		0			0
$562$	4.20321	−	17.9793i	0.177302	−	0.758412i
$563$	10.1504	−	5.86033i	0.427788	−	0.246983i	−0.270616	−	0.962687i	$-0.587227\pi$
$563$	10.1504	−	5.86033i	0.427788	−	0.246983i	0.698404	+	0.715704i	$0.253894\pi$
$564$		0			0
$565$	−0.378513	+	0.655603i	−0.0159242	+	0.0275814i
$566$	0.866059	+	2.86100i	0.0364032	+	0.120257i
$567$		0			0
$568$	16.0523	+	13.2207i	0.673538	+	0.554728i
$569$	−5.55324	+	9.61849i	−0.232804	+	0.403228i	−0.958632	−	0.284648i	$-0.908123\pi$
$569$	−5.55324	+	9.61849i	−0.232804	+	0.403228i	0.725828	+	0.687876i	$0.241457\pi$
$570$		0			0
$571$	17.7557	+	30.7537i	0.743052	+	1.28700i	0.951099	+	0.308885i	$0.0999558\pi$
$571$	17.7557	+	30.7537i	0.743052	+	1.28700i	−0.208047	+	0.978119i	$0.566711\pi$
$572$	−3.87428	−	60.1824i	−0.161992	−	2.51635i
$573$		0			0
$574$	12.1417	−	12.4978i	0.506787	−	0.521648i
$575$			6.47756i			0.270133i
$576$		0			0
$577$	−23.4304	+	13.5276i	−0.975421	+	0.563159i	−0.900885	−	0.434059i	$-0.857081\pi$
$577$	−23.4304	+	13.5276i	−0.975421	+	0.563159i	−0.0745363	+	0.997218i	$0.523748\pi$
$578$	17.3241	+	16.2447i	0.720589	+	0.675692i
$579$		0			0
$580$	−7.16193	−	10.7456i	−0.297383	−	0.446188i
$581$	4.45023	+	2.67543i	0.184627	+	0.110995i
$582$		0			0
$583$	−30.7152	−	17.7334i	−1.27209	−	0.734443i
$584$	−3.19108	+	19.1205i	−0.132048	+	0.791212i
$585$		0			0
$586$	−0.107527	+	0.459948i	−0.00444190	+	0.0190003i
$587$		−	35.3797i		−	1.46027i	−0.683300	−	0.730137i	$-0.739456\pi$
$587$		−	35.3797i		−	1.46027i	0.683300	−	0.730137i	$-0.260544\pi$
$588$		0			0
$589$		−	22.1906i		−	0.914347i
$590$	34.8895	+	8.15649i	1.43638	+	0.335797i
$591$		0			0
$592$	−4.62394	−	35.7649i	−0.190043	−	1.46993i
$593$	33.9659	+	19.6102i	1.39481	+	0.805294i	0.993843	−	0.110798i	$-0.0353406\pi$
$593$	33.9659	+	19.6102i	1.39481	+	0.805294i	0.400968	+	0.916092i	$0.368674\pi$
$594$		0			0
$595$	2.58160	+	1.55203i	0.105835	+	0.0636271i
$596$	−6.60594	−	9.91142i	−0.270590	−	0.405988i
$597$		0			0
$598$	26.3129	−	28.0613i	1.07602	−	1.14751i
$599$	41.2853	−	23.8361i	1.68687	−	0.973916i	0.729982	−	0.683466i	$-0.239528\pi$
$599$	41.2853	−	23.8361i	1.68687	−	0.973916i	0.956890	−	0.290450i	$-0.0938051\pi$
$600$		0			0
$601$			13.4207i			0.547442i	0.961809	+	0.273721i	$0.0882544\pi$
$601$			13.4207i			0.547442i	−0.961809	+	0.273721i	$0.911746\pi$
$602$	−9.84121	−	9.56086i	−0.401098	−	0.389671i
$603$		0			0
$604$	−7.17030	+	0.461592i	−0.291755	+	0.0187819i
$605$	−26.5558	−	45.9960i	−1.07965	−	1.87000i
$606$		0			0
$607$	−19.1391	+	33.1498i	−0.776831	+	1.34551i	0.156929	+	0.987610i	$0.449841\pi$
$607$	−19.1391	+	33.1498i	−0.776831	+	1.34551i	−0.933760	+	0.357901i	$0.883493\pi$
$608$	−20.7916	−	2.10885i	−0.843210	−	0.0855251i
$609$		0			0
$610$	−16.9522	+	5.13164i	−0.686376	+	0.207774i
$611$	−2.54374	+	4.40588i	−0.102909	+	0.178243i
$612$		0			0
$613$	16.9225	−	9.77021i	0.683493	−	0.394615i	−0.117677	−	0.993052i	$-0.537545\pi$
$613$	16.9225	−	9.77021i	0.683493	−	0.394615i	0.801170	+	0.598437i	$0.204211\pi$
$614$	12.9328	+	3.02343i	0.521923	+	0.122016i
$615$		0			0
$616$	27.5801	−	32.3049i	1.11123	−	1.30160i
$617$	1.16195			0.0467785			0.0233892	−	0.999726i	$-0.492554\pi$
$617$	1.16195			0.0467785			0.0233892	+	0.999726i	$0.492554\pi$
$618$		0			0
$619$	31.0842	−	17.9465i	1.24938	−	0.721330i	0.278394	−	0.960467i	$-0.410198\pi$
$619$	31.0842	−	17.9465i	1.24938	−	0.721330i	0.970986	+	0.239137i	$0.0768645\pi$
$620$	26.9530	+	13.3307i	1.08246	+	0.535375i
$621$		0			0
$622$	−21.4877	+	6.50459i	−0.861579	+	0.260810i
$623$	−15.8033	+	8.75495i	−0.633147	+	0.350759i
$624$		0			0
$625$	14.8624	−	25.7425i	0.594498	−	1.02970i
$626$	−31.1153	+	33.1827i	−1.24362	+	1.32625i
$627$		0			0
$628$	0.126368	+	1.96298i	0.00504264	+	0.0783316i
$629$	−4.10084			−0.163511
$630$		0			0
$631$		−	8.26460i		−	0.329008i	−0.986376	−	0.164504i	$-0.947398\pi$
$631$		−	8.26460i		−	0.329008i	0.986376	−	0.164504i	$-0.0526024\pi$
$632$	23.6092	−	8.83890i	0.939125	−	0.351593i
$633$		0			0
$634$	−14.7725	+	15.7540i	−0.586690	+	0.625673i
$635$	13.8677	+	8.00650i	0.550322	+	0.317728i
$636$		0			0
$637$	17.4419	+	32.8417i	0.691074	+	1.30123i
$638$	5.99955	+	19.8193i	0.237524	+	0.784655i
$639$		0			0
$640$	15.0517	−	23.9869i	0.594972	−	0.948165i
$641$	14.4955	+	25.1070i	0.572539	+	0.991666i	0.996304	+	0.0858940i	$0.0273747\pi$
$641$	14.4955	+	25.1070i	0.572539	+	0.991666i	−0.423766	+	0.905772i	$0.639292\pi$
$642$		0			0
$643$		−	39.1239i		−	1.54289i	−0.636293	−	0.771447i	$-0.719533\pi$
$643$		−	39.1239i		−	1.54289i	0.636293	−	0.771447i	$-0.280467\pi$
$644$	27.0654	−	1.26195i	1.06653	−	0.0497279i
$645$		0			0
$646$	−0.540978	+	2.31404i	−0.0212845	+	0.0910448i
$647$	−6.09491	−	10.5567i	−0.239616	−	0.415027i	0.720988	−	0.692947i	$-0.243688\pi$
$647$	−6.09491	−	10.5567i	−0.239616	−	0.415027i	−0.960604	+	0.277921i	$0.910355\pi$
$648$		0			0
$649$	−49.7577	−	28.7276i	−1.95316	−	1.12766i
$650$	9.09624	−	2.75354i	0.356784	−	0.108003i
$651$		0			0
$652$	4.19664	−	2.79705i	0.164353	−	0.109541i
$653$	−8.80194	−	5.08180i	−0.344446	−	0.198866i	0.317790	−	0.948161i	$-0.397059\pi$
$653$	−8.80194	−	5.08180i	−0.344446	−	0.198866i	−0.662237	+	0.749295i	$0.730393\pi$
$654$		0			0
$655$	−31.4368	+	18.1500i	−1.22834	+	0.709181i
$656$	−14.8047	+	11.3054i	−0.578025	+	0.441402i
$657$		0			0
$658$	−3.44746	+	0.977343i	−0.134396	+	0.0381008i
$659$	8.28558			0.322760			0.161380	−	0.986892i	$-0.448405\pi$
$659$	8.28558			0.322760			0.161380	+	0.986892i	$0.448405\pi$
$660$		0			0
$661$	8.30890	+	14.3914i	0.323179	+	0.559762i	0.981142	−	0.193288i	$-0.0619151\pi$
$661$	8.30890	+	14.3914i	0.323179	+	0.559762i	−0.657963	+	0.753050i	$0.728582\pi$
$662$	−21.7031	−	20.3509i	−0.843516	−	0.790961i
$663$		0			0
$664$	−4.28487	−	3.52903i	−0.166285	−	0.136953i
$665$	0.432875	−	24.4612i	0.0167862	−	0.948566i
$666$		0			0
$667$	−6.60439	+	11.4391i	−0.255723	+	0.442925i
$668$	−9.43384	−	4.66590i	−0.365006	−	0.180529i
$669$		0			0
$670$	−7.49614	+	32.0649i	−0.289601	+	1.23877i
$671$	28.4018			1.09644
$672$		0			0
$673$	13.1599			0.507278			0.253639	−	0.967299i	$-0.418372\pi$
$673$	13.1599			0.507278			0.253639	+	0.967299i	$0.418372\pi$
$674$	0.381012	−	1.62979i	0.0146760	−	0.0627770i
$675$		0			0
$676$	−27.2857	−	13.4953i	−1.04945	−	0.519050i
$677$	10.2201	−	17.7017i	0.392790	−	0.680332i	−0.600026	−	0.799980i	$-0.704843\pi$
$677$	10.2201	−	17.7017i	0.392790	−	0.680332i	0.992816	+	0.119648i	$0.0381766\pi$
$678$		0			0
$679$	−8.41863	−	5.06119i	−0.323077	−	0.194231i
$680$	−2.48568	−	2.04721i	−0.0953215	−	0.0785070i
$681$		0			0
$682$	−35.1731	−	32.9816i	−1.34685	−	1.26293i
$683$	−7.87273	−	13.6360i	−0.301242	−	0.521766i	0.675176	−	0.737657i	$-0.264068\pi$
$683$	−7.87273	−	13.6360i	−0.301242	−	0.521766i	−0.976418	+	0.215891i	$0.930734\pi$
$684$		0			0
$685$	−3.08150			−0.117738
$686$	−7.30713	+	25.1517i	−0.278987	+	0.960295i
$687$		0			0
$688$	8.90229	+	11.6577i	0.339397	+	0.444447i
$689$	−28.7460	+	16.5965i	−1.09514	+	0.632277i
$690$		0			0
$691$	2.76346	+	1.59549i	0.105127	+	0.0606952i	0.551642	−	0.834081i	$-0.314002\pi$
$691$	2.76346	+	1.59549i	0.105127	+	0.0606952i	−0.446515	+	0.894776i	$0.647335\pi$
$692$	−0.239022	+	0.159308i	−0.00908626	+	0.00605597i
$693$		0			0
$694$	−6.51522	+	1.97223i	−0.247314	+	0.0748650i
$695$	34.2033	+	19.7473i	1.29740	+	0.749057i
$696$		0			0
$697$	1.05912	+	1.83445i	0.0401170	+	0.0694847i
$698$	−11.4220	+	48.8578i	−0.432329	+	1.84929i
$699$		0			0
$700$	5.94674	+	3.07335i	0.224766	+	0.116162i
$701$		−	39.2121i		−	1.48102i	−0.672045	−	0.740511i	$-0.734584\pi$
$701$		−	39.2121i		−	1.48102i	0.672045	−	0.740511i	$-0.265416\pi$
$702$		0			0
$703$	16.6534	+	28.8445i	0.628094	+	1.08789i
$704$	−34.2449	+	29.8213i	−1.29065	+	1.12393i
$705$		0			0
$706$	−1.95737	−	6.46612i	−0.0736666	−	0.243356i
$707$	−15.0296	−	0.265969i	−0.565246	−	0.0100028i
$708$		0			0
$709$	33.3653	+	19.2635i	1.25306	+	0.723454i	0.971716	−	0.236153i	$-0.0758867\pi$
$709$	33.3653	+	19.2635i	1.25306	+	0.723454i	0.281343	+	0.959607i	$0.409220\pi$
$710$	17.8022	−	18.9850i	0.668103	−	0.712495i
$711$		0			0
$712$	18.0877	−	6.77174i	0.677866	−	0.253782i
$713$		−	30.7567i		−	1.15185i
$714$		0			0
$715$	−75.4744			−2.82258
$716$	2.43155	+	37.7714i	0.0908714	+	1.41158i
$717$		0			0
$718$	−35.7092	+	38.0819i	−1.33266	+	1.42120i
$719$	−11.5009	+	19.9202i	−0.428912	+	0.742897i	−0.996777	−	0.0802246i	$-0.974436\pi$
$719$	−11.5009	+	19.9202i	−0.428912	+	0.742897i	0.567865	+	0.823122i	$0.307770\pi$
$720$		0			0
$721$	−7.57341	−	13.6706i	−0.282049	−	0.509119i
$722$	−7.24417	+	2.19289i	−0.269600	+	0.0816111i
$723$		0			0
$724$	−39.8449	−	19.7070i	−1.48082	−	0.732403i
$725$	−2.82613	+	1.63166i	−0.104960	+	0.0605985i
$726$		0			0
$727$	21.8433			0.810125			0.405062	−	0.914289i	$-0.367250\pi$
$727$	21.8433			0.810125			0.405062	+	0.914289i	$0.367250\pi$
$728$	−13.2773	−	37.4707i	−0.492090	−	1.38876i
$729$		0			0
$730$	23.6234	+	5.52269i	0.874341	+	0.204404i
$731$	1.44451	−	0.833989i	0.0534272	−	0.0308462i
$732$		0			0
$733$	−24.0681	+	41.6871i	−0.888974	+	1.53975i	−0.0478850	+	0.998853i	$0.515248\pi$
$733$	−24.0681	+	41.6871i	−0.888974	+	1.53975i	−0.841089	+	0.540896i	$0.818085\pi$
$734$	0.769946	−	0.233072i	0.0284192	−	0.00860283i
$735$		0			0
$736$	−28.8177	−	2.92292i	−1.06223	−	0.107740i
$737$	26.4018	−	45.7293i	0.972524	−	1.68446i
$738$		0			0
$739$	3.23455	+	5.60241i	0.118985	+	0.206088i	0.919366	−	0.393404i	$-0.128703\pi$
$739$	3.23455	+	5.60241i	0.118985	+	0.206088i	−0.800381	+	0.599492i	$0.795369\pi$
$740$	−45.0392	+	2.89943i	−1.65567	+	0.106585i
$741$		0			0
$742$	−22.6677	−	5.72407i	−0.832156	−	0.210137i
$743$		−	16.6709i		−	0.611597i	−0.952096	−	0.305798i	$-0.901077\pi$
$743$		−	16.6709i		−	0.611597i	0.952096	−	0.305798i	$-0.0989234\pi$
$744$		0			0
$745$	−12.9097	+	7.45340i	−0.472974	+	0.273072i
$746$	22.6671	−	24.1732i	0.829900	−	0.885043i
$747$		0			0
$748$	2.86381	+	4.29681i	0.104711	+	0.157107i
$749$	13.6686	+	24.6729i	0.499441	+	0.901528i
$750$		0			0
$751$	21.2698	+	12.2801i	0.776145	+	0.448108i	0.835062	−	0.550155i	$-0.185431\pi$
$751$	21.2698	+	12.2801i	0.776145	+	0.448108i	−0.0589171	+	0.998263i	$0.518765\pi$
$752$	3.79911	−	0.491175i	0.138539	−	0.0179113i
$753$		0			0
$754$	18.8711	+	4.41170i	0.687245	+	0.160664i
$755$			8.99223i			0.327261i
$756$		0			0
$757$		−	2.80888i		−	0.102091i	−0.998696	−	0.0510453i	$-0.983745\pi$
$757$		−	2.80888i		−	0.102091i	0.998696	−	0.0510453i	$-0.0162553\pi$
$758$	−4.74016	+	20.2761i	−0.172171	+	0.736462i
$759$		0			0
$760$	−4.30542	+	25.7974i	−0.156174	+	0.935772i
$761$	17.4708	+	10.0868i	0.633317	+	0.365646i	0.782036	−	0.623234i	$-0.214181\pi$
$761$	17.4708	+	10.0868i	0.633317	+	0.365646i	−0.148718	+	0.988880i	$0.547515\pi$
$762$		0			0
$763$	0.148823	−	8.40982i	0.00538776	−	0.304456i
$764$	−13.0786	−	19.6228i	−0.473166	−	0.709929i
$765$		0			0
$766$	−5.15303	−	4.83197i	−0.186187	−	0.174586i
$767$	−46.5677	+	26.8859i	−1.68146	+	0.970792i
$768$		0			0
$769$			32.1388i			1.15895i	0.814988	+	0.579477i	$0.196743\pi$
$769$			32.1388i			1.15895i	−0.814988	+	0.579477i	$0.803257\pi$
$770$	−38.1288	−	37.0426i	−1.37407	−	1.33492i
$771$		0			0
$772$	3.44629	+	53.5341i	0.124035	+	1.92673i
$773$	11.2931	+	19.5603i	0.406186	+	0.703534i	0.994459	−	0.105128i	$-0.0335253\pi$
$773$	11.2931	+	19.5603i	0.406186	+	0.703534i	−0.588273	+	0.808662i	$0.700192\pi$
$774$		0			0
$775$	3.79934	−	6.58065i	0.136476	−	0.236384i
$776$	8.10583	+	6.67598i	0.290982	+	0.239654i
$777$		0			0
$778$	−13.0628	−	43.1528i	−0.468326	−	1.54710i
$779$	8.60209	−	14.8993i	0.308202	−	0.533822i
$780$		0			0
$781$	−36.1423	+	20.8668i	−1.29327	+	0.746673i
$782$	−0.749810	+	3.20732i	−0.0268131	+	0.114694i
$783$		0			0
$784$	11.6829	−	25.4462i	0.417247	−	0.908793i
$785$	2.46177			0.0878642
$786$		0			0
$787$	−29.2593	+	16.8929i	−1.04298	+	0.602166i	−0.920677	−	0.390326i	$-0.872362\pi$
$787$	−29.2593	+	16.8929i	−1.04298	+	0.602166i	−0.122306	+	0.992492i	$0.539029\pi$
$788$	14.7046	−	29.7307i	0.523828	−	1.05911i
$789$		0			0
$790$	−9.14088	−	30.1967i	−0.325218	−	1.07435i
$791$	0.412298	−	0.685804i	0.0146596	−	0.0243844i
$792$		0			0
$793$	13.2905	−	23.0197i	0.471958	−	0.817455i
$794$	−33.9466	−	31.8315i	−1.20472	−	1.12966i
$795$		0			0
$796$	−1.46581	−	22.7697i	−0.0519543	−	0.807049i
$797$	−27.0472			−0.958061			−0.479030	−	0.877798i	$-0.659012\pi$
$797$	−27.0472			−0.958061			−0.479030	+	0.877798i	$0.659012\pi$
$798$		0			0
$799$		−	0.435609i		−	0.0154108i
$800$	−5.80471	−	4.18519i	−0.205228	−	0.147969i
$801$		0			0
$802$	−0.219191	−	0.205534i	−0.00773989	−	0.00725765i
$803$	−33.6905	−	19.4512i	−1.18891	−	0.686418i
$804$		0			0
$805$	0.599976	−	33.9039i	0.0211464	−	1.19496i
$806$	−43.1907	+	13.0743i	−1.52133	+	0.460524i
$807$		0			0
$808$	15.8506	+	2.64536i	0.557622	+	0.0930634i
$809$	−24.9224	−	43.1669i	−0.876226	−	1.51767i	−0.855451	−	0.517884i	$-0.826720\pi$
$809$	−24.9224	−	43.1669i	−0.876226	−	1.51767i	−0.0207751	−	0.999784i	$-0.506613\pi$
$810$		0			0
$811$		−	36.5330i		−	1.28285i	−0.767188	−	0.641423i	$-0.778345\pi$
$811$		−	36.5330i		−	1.28285i	0.767188	−	0.641423i	$-0.221655\pi$
$812$	7.36822	+	11.4906i	0.258574	+	0.403241i
$813$		0			0
$814$	70.4715	+	16.4749i	2.47003	+	0.577444i
$815$	−3.15588	−	5.46614i	−0.110546	−	0.191470i
$816$		0			0
$817$	−11.7322	−	6.77360i	−0.410459	−	0.236978i
$818$	−8.38793	−	27.7093i	−0.293277	−	0.968832i
$819$		0			0
$820$	12.9292	+	19.3988i	0.451509	+	0.677435i
$821$	2.59911	+	1.50060i	0.0907095	+	0.0523711i	0.544669	−	0.838651i	$-0.316655\pi$
$821$	2.59911	+	1.50060i	0.0907095	+	0.0523711i	−0.453959	+	0.891023i	$0.649989\pi$
$822$		0			0
$823$	13.8543	−	7.99877i	0.482930	−	0.278820i	−0.238707	−	0.971092i	$-0.576723\pi$
$823$	13.8543	−	7.99877i	0.482930	−	0.278820i	0.721637	+	0.692272i	$0.243390\pi$
$824$	5.85785	+	15.6467i	0.204068	+	0.545078i
$825$		0			0
$826$	−36.7209	−	9.27282i	−1.27768	−	0.322643i
$827$	−4.57856			−0.159212			−0.0796060	−	0.996826i	$-0.525366\pi$
$827$	−4.57856			−0.159212			−0.0796060	+	0.996826i	$0.525366\pi$
$828$		0			0
$829$	−1.53077	−	2.65136i	−0.0531657	−	0.0920857i	0.838218	−	0.545336i	$-0.183598\pi$
$829$	−1.53077	−	2.65136i	−0.0531657	−	0.0920857i	−0.891383	+	0.453250i	$0.850264\pi$
$830$	−4.75198	+	5.06772i	−0.164943	+	0.175903i
$831$		0			0
$832$	8.14552	+	41.7103i	0.282395	+	1.44605i
$833$	−2.69938	−	1.68857i	−0.0935279	−	0.0585054i
$834$		0			0
$835$	−6.58581	+	11.4070i	−0.227911	+	0.394754i
$836$	18.5930	−	37.5927i	0.643054	−	1.30017i
$837$		0			0
$838$	−16.3101	−	3.81298i	−0.563422	−	0.131717i
$839$	39.0864			1.34941			0.674706	−	0.738087i	$-0.264270\pi$
$839$	39.0864			1.34941			0.674706	+	0.738087i	$0.264270\pi$
$840$		0			0
$841$	22.3456			0.770536
$842$	−30.0105	−	7.01586i	−1.03423	−	0.241782i
$843$		0			0
$844$	7.40929	+	3.66458i	0.255038	+	0.126140i
$845$	−19.0483	+	32.9926i	−0.655281	+	1.13498i
$846$		0			0
$847$	27.2056	+	49.1081i	0.934795	+	1.68738i
$848$	23.0686	+	9.61825i	0.792179	+	0.330292i
$849$		0			0
$850$	−0.556624	+	0.593610i	−0.0190921	+	0.0203606i
$851$	23.0820	+	39.9792i	0.791241	+	1.37047i
$852$		0			0
$853$	−26.4897			−0.906989			−0.453495	−	0.891259i	$-0.649823\pi$
$853$	−26.4897			−0.906989			−0.453495	+	0.891259i	$0.649823\pi$
$854$	18.0122	−	5.10640i	0.616364	−	0.174737i
$855$		0			0
$856$	−10.5723	−	28.2394i	−0.361355	−	0.965202i
$857$	−38.9066	+	22.4627i	−1.32902	+	0.767312i	−0.985149	−	0.171703i	$-0.945073\pi$
$857$	−38.9066	+	22.4627i	−1.32902	+	0.767312i	−0.343875	+	0.939015i	$0.611740\pi$
$858$		0			0
$859$	30.6621	+	17.7028i	1.04618	+	0.604011i	0.921577	−	0.388196i	$-0.126902\pi$
$859$	30.6621	+	17.7028i	1.04618	+	0.604011i	0.124601	+	0.992207i	$0.460235\pi$
$860$	15.2753	−	10.1810i	0.520883	−	0.347168i
$861$		0			0
$862$	−6.77677	−	22.3869i	−0.230818	−	0.762499i
$863$	−2.40437	−	1.38816i	−0.0818456	−	0.0472536i	0.458519	−	0.888685i	$-0.348380\pi$
$863$	−2.40437	−	1.38816i	−0.0818456	−	0.0472536i	−0.540364	+	0.841431i	$0.681714\pi$
$864$		0			0
$865$	0.179745	+	0.311328i	0.00611151	+	0.0105855i
$866$	54.0814	+	12.6432i	1.83776	+	0.429632i
$867$		0			0
$868$	−28.2363	−	14.5929i	−0.958402	−	0.495314i
$869$			50.5915i			1.71620i
$870$		0			0
$871$	−24.7092	−	42.7976i	−0.837239	−	1.45014i
$872$	−1.48021	+	8.86922i	−0.0501263	+	0.300350i
$873$		0			0
$874$	25.6046	−	7.75082i	0.866089	−	0.262175i
$875$	−12.7441	+	21.1982i	−0.430830	+	0.716631i
$876$		0			0
$877$	−14.3264	−	8.27135i	−0.483768	−	0.279304i	0.238217	−	0.971212i	$-0.423437\pi$
$877$	−14.3264	−	8.27135i	−0.483768	−	0.279304i	−0.721986	+	0.691908i	$0.756770\pi$
$878$	32.0144	+	30.0197i	1.08043	+	1.01312i
$879$		0			0
$880$	34.4910	+	45.1667i	1.16269	+	1.52257i
$881$			24.6158i			0.829327i	0.909975	+	0.414664i	$0.136101\pi$
$881$			24.6158i			0.829327i	−0.909975	+	0.414664i	$0.863899\pi$
$882$		0			0
$883$	40.4623			1.36167			0.680833	−	0.732439i	$-0.261618\pi$
$883$	40.4623			1.36167			0.680833	+	0.732439i	$0.261618\pi$
$884$	4.82269	−	0.310463i	0.162204	−	0.0104420i
$885$		0			0
$886$	0.871646	+	0.817338i	0.0292835	+	0.0274590i
$887$	−4.64231	+	8.04072i	−0.155873	+	0.269981i	−0.933377	−	0.358898i	$-0.883153\pi$
$887$	−4.64231	+	8.04072i	−0.155873	+	0.269981i	0.777503	+	0.628879i	$0.216486\pi$
$888$		0			0
$889$	−14.5065	−	8.72114i	−0.486532	−	0.292498i
$890$	−7.00309	−	23.1345i	−0.234744	−	0.775471i
$891$		0			0
$892$	32.4595	+	16.0542i	1.08682	+	0.537535i
$893$	−3.06399	+	1.76900i	−0.102533	+	0.0591972i
$894$		0			0
$895$	47.3688			1.58337
$896$	−16.3563	+	25.0694i	−0.546424	+	0.837509i
$897$		0			0
$898$	13.4386	−	57.4840i	0.448453	−	1.91827i
$899$	13.4190	−	7.74746i	0.447548	−	0.258392i
$900$		0			0
$901$	1.42106	−	2.46134i	0.0473423	−	0.0819993i
$902$	−10.8308	−	35.7793i	−0.360627	−	1.19132i
$903$		0			0
$904$	−0.543843	+	0.660322i	−0.0180880	+	0.0219620i
$905$	−27.8159	+	48.1786i	−0.924632	+	1.60151i
$906$		0			0
$907$	−2.55327	−	4.42240i	−0.0847800	−	0.146843i	0.820517	−	0.571621i	$-0.193685\pi$
$907$	−2.55327	−	4.42240i	−0.0847800	−	0.146843i	−0.905297	+	0.424778i	$0.860352\pi$
$908$	15.8177	−	1.01827i	0.524928	−	0.0337925i
$909$		0			0
$910$	−47.8653	+	13.5697i	−1.58672	+	0.449830i
$911$		−	36.3702i		−	1.20500i	−0.798119	−	0.602500i	$-0.794171\pi$
$911$		−	36.3702i		−	1.20500i	0.798119	−	0.602500i	$-0.205829\pi$
$912$		0			0
$913$	9.64757	−	5.57003i	0.319288	−	0.184341i
$914$	−7.72242	−	7.24127i	−0.255435	−	0.239520i
$915$		0			0
$916$	−3.58764	+	2.39115i	−0.118539	+	0.0790059i
$917$	33.5639	−	18.5942i	1.10838	−	0.614034i
$918$		0			0
$919$	40.4248	+	23.3393i	1.33349	+	0.769892i	0.985833	−	0.167729i	$-0.0536433\pi$
$919$	40.4248	+	23.3393i	1.33349	+	0.769892i	0.347659	+	0.937621i	$0.386977\pi$
$920$	−5.96742	+	35.7559i	−0.196740	+	1.17884i
$921$		0			0
$922$	−1.39559	+	5.96964i	−0.0459612	+	0.196600i
$923$			39.0580i			1.28561i
$924$		0			0
$925$			11.4052i			0.375000i
$926$	−48.6386	−	11.3708i	−1.59836	−	0.373666i
$927$		0			0
$928$	−5.98378	−	13.3093i	−0.196427	−	0.436898i
$929$	−33.8671	−	19.5532i	−1.11114	−	0.641518i	−0.172017	−	0.985094i	$-0.555028\pi$
$929$	−33.8671	−	19.5532i	−1.11114	−	0.641518i	−0.939125	+	0.343576i	$0.888362\pi$
$930$		0			0
$931$	−0.914979	+	25.8441i	−0.0299872	+	0.847006i
$932$	33.3086	−	22.2001i	1.09106	−	0.727188i
$933$		0			0
$934$	−10.1559	+	10.8307i	−0.332310	+	0.354390i
$935$	5.59661	−	3.23121i	0.183029	−	0.105672i
$936$		0			0
$937$			14.4038i			0.470551i	0.971929	+	0.235275i	$0.0755992\pi$
$937$			14.4038i			0.470551i	−0.971929	+	0.235275i	$0.924401\pi$
$938$	8.52210	−	33.7480i	0.278256	−	1.10191i
$939$		0			0
$940$	−0.307990	−	4.78427i	−0.0100455	−	0.156046i
$941$	13.1269	+	22.7364i	0.427924	+	0.741186i	0.996688	−	0.0813146i	$-0.0259118\pi$
$941$	13.1269	+	22.7364i	0.427924	+	0.741186i	−0.568765	+	0.822500i	$0.692579\pi$
$942$		0			0
$943$	11.9227	−	20.6508i	0.388257	−	0.672482i
$944$	37.3704	+	15.5813i	1.21630	+	0.507128i
$945$		0			0
$946$	−28.1739	+	8.52858i	−0.916014	+	0.277288i
$947$	7.85354	−	13.6027i	0.255206	−	0.442030i	−0.709746	−	0.704458i	$-0.751190\pi$
$947$	7.85354	−	13.6027i	0.255206	−	0.442030i	0.964951	+	0.262429i	$0.0845234\pi$
$948$		0			0
$949$	−31.5306	+	18.2042i	−1.02353	+	0.590933i
$950$	6.43576	+	1.50456i	0.208804	+	0.0488142i
$951$		0			0
$952$	2.58874	+	2.21011i	0.0839015	+	0.0716302i
$953$	−42.8466			−1.38794			−0.693968	−	0.720006i	$-0.744139\pi$
$953$	−42.8466			−1.38794			−0.693968	+	0.720006i	$0.744139\pi$
$954$		0			0
$955$	−25.5588	+	14.7564i	−0.827064	+	0.477506i
$956$	−16.7511	+	33.8686i	−0.541770	+	1.09539i
$957$		0			0
$958$	−22.9123	+	6.93583i	−0.740264	+	0.224087i
$959$	3.25672	+	0.0576322i	0.105165	+	0.00186104i
$960$		0			0
$961$	−2.53999	+	4.39939i	−0.0819352	+	0.141916i
$962$	46.3297	−	49.4081i	1.49373	−	1.59298i
$963$		0			0
$964$	36.5410	−	2.35235i	1.17691	−	0.0757641i
$965$	67.1368			2.16121
$966$		0			0
$967$			0.672082i			0.0216127i	0.999942	+	0.0108063i	$0.00343983\pi$
$967$			0.672082i			0.0216127i	−0.999942	+	0.0108063i	$0.996560\pi$
$968$	−21.0429	−	56.2068i	−0.676343	−	1.80655i
$969$		0			0
$970$	8.98945	−	9.58676i	0.288634	−	0.307812i
$971$	6.45838	+	3.72875i	0.207259	+	0.119661i	0.600037	−	0.799972i	$-0.295153\pi$
$971$	6.45838	+	3.72875i	0.207259	+	0.119661i	−0.392778	+	0.919633i	$0.628486\pi$
$972$		0			0
$973$	−35.7789	−	21.5099i	−1.14702	−	0.689575i
$974$	−9.72184	−	32.1158i	−0.311508	−	1.02906i
$975$		0			0
$976$	−19.8495	+	2.56628i	−0.635366	+	0.0821446i
$977$	8.78701	+	15.2195i	0.281121	+	0.486916i	0.971661	−	0.236378i	$-0.0759603\pi$
$977$	8.78701	+	15.2195i	0.281121	+	0.486916i	−0.690540	+	0.723294i	$0.742627\pi$
$978$		0			0
$979$			38.7596i			1.23876i
$980$	−30.8409	−	16.6369i	−0.985177	−	0.531446i
$981$		0			0
$982$	1.09843	−	4.69857i	0.0350525	−	0.149938i
$983$	21.3661	+	37.0072i	0.681472	+	1.18034i	0.974532	+	0.224250i	$0.0719934\pi$
$983$	21.3661	+	37.0072i	0.681472	+	1.18034i	−0.293059	+	0.956094i	$0.594673\pi$
$984$		0			0
$985$	−35.9489	−	20.7551i	−1.14543	−	0.661313i
$986$	−1.58821	+	0.480770i	−0.0505790	+	0.0153108i
$987$		0			0
$988$	−21.7685	−	32.6610i	−0.692548	−	1.03909i
$989$	−16.2612	−	9.38839i	−0.517075	−	0.298533i
$990$		0			0
$991$	39.3373	−	22.7114i	1.24959	−	0.721451i	0.278563	−	0.960418i	$-0.410142\pi$
$991$	39.3373	−	22.7114i	1.24959	−	0.721451i	0.971028	+	0.238967i	$0.0768087\pi$
$992$	27.5619	+	19.8721i	0.875091	+	0.630940i
$993$		0			0
$994$	−19.1695	+	19.7316i	−0.608020	+	0.625850i
$995$	−28.5553			−0.905264
$996$		0			0
$997$	−21.8718	−	37.8831i	−0.692687	−	1.19977i	−0.970954	−	0.239265i	$-0.923094\pi$
$997$	−21.8718	−	37.8831i	−0.692687	−	1.19977i	0.278268	−	0.960504i	$-0.410240\pi$
$998$	−18.0121	−	16.8898i	−0.570162	−	0.534638i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.9		32
3.2	odd	2		168.2.t.a.19.8	yes	32
4.3	odd	2		2016.2.bs.c.271.4		32
7.3	odd	6	inner	504.2.bk.c.451.13		32
8.3	odd	2	inner	504.2.bk.c.19.13		32
8.5	even	2		2016.2.bs.c.271.13		32
12.11	even	2		672.2.bb.a.271.7		32
21.2	odd	6		1176.2.p.a.979.26		32
21.5	even	6		1176.2.p.a.979.25		32
21.17	even	6		168.2.t.a.115.4	yes	32
24.5	odd	2		672.2.bb.a.271.2		32
24.11	even	2		168.2.t.a.19.4	✓	32
28.3	even	6		2016.2.bs.c.1711.13		32
56.3	even	6	inner	504.2.bk.c.451.9		32
56.45	odd	6		2016.2.bs.c.1711.4		32
84.23	even	6		4704.2.p.a.3919.15		32
84.47	odd	6		4704.2.p.a.3919.2		32
84.59	odd	6		672.2.bb.a.367.2		32
168.5	even	6		4704.2.p.a.3919.16		32
168.59	odd	6		168.2.t.a.115.8	yes	32
168.101	even	6		672.2.bb.a.367.7		32
168.107	even	6		1176.2.p.a.979.27		32
168.131	odd	6		1176.2.p.a.979.28		32
168.149	odd	6		4704.2.p.a.3919.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.4	✓	32	24.11	even	2
168.2.t.a.19.8	yes	32	3.2	odd	2
168.2.t.a.115.4	yes	32	21.17	even	6
168.2.t.a.115.8	yes	32	168.59	odd	6
504.2.bk.c.19.9		32	1.1	even	1	trivial
504.2.bk.c.19.13		32	8.3	odd	2	inner
504.2.bk.c.451.9		32	56.3	even	6	inner
504.2.bk.c.451.13		32	7.3	odd	6	inner
672.2.bb.a.271.2		32	24.5	odd	2
672.2.bb.a.271.7		32	12.11	even	2
672.2.bb.a.367.2		32	84.59	odd	6
672.2.bb.a.367.7		32	168.101	even	6
1176.2.p.a.979.25		32	21.5	even	6
1176.2.p.a.979.26		32	21.2	odd	6
1176.2.p.a.979.27		32	168.107	even	6
1176.2.p.a.979.28		32	168.131	odd	6
2016.2.bs.c.271.4		32	4.3	odd	2
2016.2.bs.c.271.13		32	8.5	even	2
2016.2.bs.c.1711.4		32	56.45	odd	6
2016.2.bs.c.1711.13		32	28.3	even	6
4704.2.p.a.3919.1		32	168.149	odd	6
4704.2.p.a.3919.2		32	84.47	odd	6
4704.2.p.a.3919.15		32	84.23	even	6
4704.2.p.a.3919.16		32	168.5	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.321935 - 1.37708i) q^{2} +(-1.79272 - 0.886663i) q^{4} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(-1.79815 + 2.18327i) q^{8} +O(q^{10})\)	\(q+(0.321935 - 1.37708i) q^{2} +(-1.79272 - 0.886663i) q^{4} +(-1.25150 + 2.16767i) q^{5} +(1.36321 - 2.26752i) q^{7} +(-1.79815 + 2.18327i) q^{8} +(2.58215 + 2.42127i) q^{10} +(-2.83809 - 4.91572i) q^{11} -5.31228 q^{13} +(-2.68370 - 2.60725i) q^{14} +(2.42766 + 3.17907i) q^{16} +(0.393919 - 0.227429i) q^{17} +(-3.19938 - 1.84716i) q^{19} +(4.16558 - 2.77635i) q^{20} +(-7.68304 + 2.32575i) q^{22} +(-4.43443 - 2.56022i) q^{23} +(-0.632521 - 1.09556i) q^{25} +(-1.71021 + 7.31545i) q^{26} +(-4.45438 + 2.85632i) q^{28} -2.57962i q^{29} +(3.00333 + 5.20192i) q^{31} +(5.15939 - 2.31963i) q^{32} +(-0.186372 - 0.615676i) q^{34} +(3.20917 + 5.79280i) q^{35} +(-7.80778 - 4.50782i) q^{37} +(-3.57369 + 3.81115i) q^{38} +(-2.48222 - 6.63015i) q^{40} +4.65692i q^{41} +3.66703 q^{43} +(0.729306 + 11.3289i) q^{44} +(-4.95323 + 5.28235i) q^{46} +(0.478841 - 0.829377i) q^{47} +(-3.28332 - 6.18222i) q^{49} +(-1.71230 + 0.518335i) q^{50} +(9.52341 + 4.71020i) q^{52} +(5.41124 - 3.12418i) q^{53} +14.2075 q^{55} +(2.49936 + 7.05359i) q^{56} +(-3.55235 - 0.830471i) q^{58} +(8.76604 - 5.06108i) q^{59} +(-2.50184 + 4.33331i) q^{61} +(8.13036 - 2.46115i) q^{62} +(-1.53334 - 7.85168i) q^{64} +(6.64834 - 11.5153i) q^{65} +(4.65133 + 8.05634i) q^{67} +(-0.907837 + 0.0584425i) q^{68} +(9.01031 - 2.55439i) q^{70} -7.35240i q^{71} +(5.93541 - 3.42681i) q^{73} +(-8.72125 + 9.30073i) q^{74} +(4.09777 + 6.14821i) q^{76} +(-15.0154 - 0.265718i) q^{77} +(-7.71882 - 4.45646i) q^{79} +(-9.92938 + 1.28374i) q^{80} +(6.41297 + 1.49923i) q^{82} +1.96259i q^{83} +1.13851i q^{85} +(1.18055 - 5.04980i) q^{86} +(15.8357 + 2.64286i) q^{88} +(-5.91361 - 3.41423i) q^{89} +(-7.24175 + 12.0457i) q^{91} +(5.67961 + 8.52158i) q^{92} +(-0.987965 - 0.926409i) q^{94} +(8.00807 - 4.62346i) q^{95} -3.71270i q^{97} +(-9.57044 + 2.53113i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} - 18 q^{10} - 8 q^{11} + 10 q^{14} + 6 q^{16} - 20 q^{22} - 16 q^{25} + 30 q^{26} - 14 q^{28} + 12 q^{32} + 24 q^{35} + 18 q^{38} - 30 q^{40} - 16 q^{43} - 24 q^{44} + 8 q^{46} + 8 q^{49} - 76 q^{50} + 36 q^{52} - 16 q^{56} - 6 q^{58} + 96 q^{59} + 76 q^{64} - 32 q^{67} - 96 q^{68} + 6 q^{70} - 24 q^{73} + 34 q^{74} - 36 q^{80} - 36 q^{82} - 50 q^{86} - 14 q^{88} + 56 q^{91} + 128 q^{92} + 36 q^{94} - 60 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 - 18 * q^10 - 8 * q^11 + 10 * q^14 + 6 * q^16 - 20 * q^22 - 16 * q^25 + 30 * q^26 - 14 * q^28 + 12 * q^32 + 24 * q^35 + 18 * q^38 - 30 * q^40 - 16 * q^43 - 24 * q^44 + 8 * q^46 + 8 * q^49 - 76 * q^50 + 36 * q^52 - 16 * q^56 - 6 * q^58 + 96 * q^59 + 76 * q^64 - 32 * q^67 - 96 * q^68 + 6 * q^70 - 24 * q^73 + 34 * q^74 - 36 * q^80 - 36 * q^82 - 50 * q^86 - 14 * q^88 + 56 * q^91 + 128 * q^92 + 36 * q^94 - 60 * q^98

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