LMFDB - Embedded newform 504.2.bk.c.19.15

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			19.15
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.c.451.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40727 - 0.139971i) q^{2} +(1.96082 - 0.393955i) q^{4} +(-0.128707 + 0.222928i) q^{5} +(0.623918 - 2.57113i) q^{7} +(2.70425 - 0.828860i) q^{8} +O(q^{10})$	\(q+(1.40727 - 0.139971i) q^{2} +(1.96082 - 0.393955i) q^{4} +(-0.128707 + 0.222928i) q^{5} +(0.623918 - 2.57113i) q^{7} +(2.70425 - 0.828860i) q^{8} +(-0.149923 + 0.331735i) q^{10} +(-1.79412 - 3.10751i) q^{11} +4.57992 q^{13} +(0.518136 - 3.70561i) q^{14} +(3.68960 - 1.54495i) q^{16} +(-6.92813 + 3.99996i) q^{17} +(0.201988 + 0.116618i) q^{19} +(-0.164548 + 0.487825i) q^{20} +(-2.95978 - 4.12198i) q^{22} +(5.76102 + 3.32613i) q^{23} +(2.46687 + 4.27274i) q^{25} +(6.44518 - 0.641058i) q^{26} +(0.210478 - 5.28731i) q^{28} -2.80806i q^{29} +(1.03380 + 1.79060i) q^{31} +(4.97601 - 2.69060i) q^{32} +(-9.18987 + 6.59876i) q^{34} +(0.492874 + 0.470013i) q^{35} +(-6.46587 - 3.73307i) q^{37} +(0.300574 + 0.135840i) q^{38} +(-0.163282 + 0.709534i) q^{40} +4.55693i q^{41} -5.42738 q^{43} +(-4.74216 - 5.38645i) q^{44} +(8.57287 + 3.87438i) q^{46} +(-1.42355 + 2.46565i) q^{47} +(-6.22145 - 3.20835i) q^{49} +(4.06961 + 5.66761i) q^{50} +(8.98037 - 1.80428i) q^{52} +(-1.93137 + 1.11508i) q^{53} +0.923668 q^{55} +(-0.443874 - 7.47014i) q^{56} +(-0.393048 - 3.95170i) q^{58} +(-2.14701 + 1.23958i) q^{59} +(-4.44251 + 7.69466i) q^{61} +(1.70547 + 2.37515i) q^{62} +(6.62598 - 4.48289i) q^{64} +(-0.589469 + 1.02099i) q^{65} +(-0.867859 - 1.50318i) q^{67} +(-12.0090 + 10.5726i) q^{68} +(0.759395 + 0.592446i) q^{70} -8.97302i q^{71} +(-6.57828 + 3.79797i) q^{73} +(-9.62174 - 4.34840i) q^{74} +(0.442003 + 0.149092i) q^{76} +(-9.10921 + 2.67409i) q^{77} +(7.51791 + 4.34047i) q^{79} +(-0.130467 + 1.02136i) q^{80} +(0.637840 + 6.41283i) q^{82} +3.79017i q^{83} -2.05930i q^{85} +(-7.63778 + 0.759678i) q^{86} +(-7.42745 - 6.91643i) q^{88} +(2.25065 + 1.29941i) q^{89} +(2.85749 - 11.7756i) q^{91} +(12.6066 + 4.25234i) q^{92} +(-1.65819 + 3.66910i) q^{94} +(-0.0519946 + 0.0300191i) q^{95} +14.6024i q^{97} +(-9.20434 - 3.64419i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.40727	−	0.139971i	0.995090	−	0.0989748i
$2$	1.40727	−	0.139971i	0.995090	−	0.0989748i
$3$		0			0
$3$		0			0
$4$	1.96082	−	0.393955i	0.980408	−	0.196978i
$5$	−0.128707	+	0.222928i	−0.0575597	+	0.0996963i	−0.893369	−	0.449323i	$-0.851665\pi$
$5$	−0.128707	+	0.222928i	−0.0575597	+	0.0996963i	0.835810	+	0.549019i	$0.184999\pi$
$6$		0			0
$7$	0.623918	−	2.57113i	0.235819	−	0.971797i
$7$	0.623918	−	2.57113i	0.235819	−	0.971797i
$8$	2.70425	−	0.828860i	0.956098	−	0.293046i
$9$		0			0
$10$	−0.149923	+	0.331735i	−0.0474097	+	0.104904i
$11$	−1.79412	−	3.10751i	−0.540948	−	0.936950i	−0.998850	−	0.0479470i	$-0.984732\pi$
$11$	−1.79412	−	3.10751i	−0.540948	−	0.936950i	0.457902	−	0.889003i	$-0.348601\pi$
$12$		0			0
$13$	4.57992			1.27024			0.635120	−	0.772413i	$-0.280951\pi$
$13$	4.57992			1.27024			0.635120	+	0.772413i	$0.280951\pi$
$14$	0.518136	−	3.70561i	0.138478	−	0.990366i
$15$		0			0
$16$	3.68960	−	1.54495i	0.922400	−	0.386237i
$17$	−6.92813	+	3.99996i	−1.68032	+	0.970132i	−0.718871	+	0.695143i	$0.755341\pi$
$17$	−6.92813	+	3.99996i	−1.68032	+	0.970132i	−0.961447	+	0.274989i	$0.911326\pi$
$18$		0			0
$19$	0.201988	+	0.116618i	0.0463391	+	0.0267539i	0.522991	−	0.852338i	$-0.324816\pi$
$19$	0.201988	+	0.116618i	0.0463391	+	0.0267539i	−0.476651	+	0.879092i	$0.658150\pi$
$20$	−0.164548	+	0.487825i	−0.0367941	+	0.109081i
$21$		0			0
$22$	−2.95978	−	4.12198i	−0.631027	−	0.878809i
$23$	5.76102	+	3.32613i	1.20126	+	0.693545i	0.960834	−	0.277124i	$-0.0893811\pi$
$23$	5.76102	+	3.32613i	1.20126	+	0.693545i	0.240421	+	0.970669i	$0.422714\pi$
$24$		0			0
$25$	2.46687	+	4.27274i	0.493374	+	0.854548i
$26$	6.44518	−	0.641058i	1.26400	−	0.125722i
$27$		0			0
$28$	0.210478	−	5.28731i	0.0397766	−	0.999209i
$29$		−	2.80806i		−	0.521444i	−0.965414	−	0.260722i	$-0.916039\pi$
$29$		−	2.80806i		−	0.521444i	0.965414	−	0.260722i	$-0.0839605\pi$
$30$		0			0
$31$	1.03380	+	1.79060i	0.185676	+	0.321600i	0.943804	−	0.330505i	$-0.107219\pi$
$31$	1.03380	+	1.79060i	0.185676	+	0.321600i	−0.758128	+	0.652106i	$0.773886\pi$
$32$	4.97601	−	2.69060i	0.879643	−	0.475635i
$33$		0			0
$34$	−9.18987	+	6.59876i	−1.57605	+	1.13168i
$35$	0.492874	+	0.470013i	0.0833109	+	0.0794466i
$36$		0			0
$37$	−6.46587	−	3.73307i	−1.06298	−	0.613713i	−0.136726	−	0.990609i	$-0.543658\pi$
$37$	−6.46587	−	3.73307i	−1.06298	−	0.613713i	−0.926256	+	0.376896i	$0.876991\pi$
$38$	0.300574	+	0.135840i	0.0487596	+	0.0220361i
$39$		0			0
$40$	−0.163282	+	0.709534i	−0.0258171	+	0.112187i
$41$			4.55693i			0.711673i	0.934548	+	0.355837i	$0.115804\pi$
$41$			4.55693i			0.711673i	−0.934548	+	0.355837i	$0.884196\pi$
$42$		0			0
$43$	−5.42738			−0.827667			−0.413834	−	0.910353i	$-0.635810\pi$
$43$	−5.42738			−0.827667			−0.413834	+	0.910353i	$0.635810\pi$
$44$	−4.74216	−	5.38645i	−0.714908	−	0.812038i
$45$		0			0
$46$	8.57287	+	3.87438i	1.26400	+	0.571246i
$47$	−1.42355	+	2.46565i	−0.207646	+	0.359653i	−0.950972	−	0.309276i	$-0.899913\pi$
$47$	−1.42355	+	2.46565i	−0.207646	+	0.359653i	0.743327	+	0.668928i	$0.233247\pi$
$48$		0			0
$49$	−6.22145	−	3.20835i	−0.888779	−	0.458336i
$50$	4.06961	+	5.66761i	0.575530	+	0.801521i
$51$		0			0
$52$	8.98037	−	1.80428i	1.24535	−	0.250209i
$53$	−1.93137	+	1.11508i	−0.265295	+	0.153168i	−0.626747	−	0.779222i	$-0.715614\pi$
$53$	−1.93137	+	1.11508i	−0.265295	+	0.153168i	0.361453	+	0.932390i	$0.382281\pi$
$54$		0			0
$55$	0.923668			0.124547
$56$	−0.443874	−	7.47014i	−0.0593152	−	0.998239i
$57$		0			0
$58$	−0.393048	−	3.95170i	−0.0516098	−	0.518883i
$59$	−2.14701	+	1.23958i	−0.279517	+	0.161379i	−0.633205	−	0.773984i	$-0.718261\pi$
$59$	−2.14701	+	1.23958i	−0.279517	+	0.161379i	0.353688	+	0.935364i	$0.384928\pi$
$60$		0			0
$61$	−4.44251	+	7.69466i	−0.568806	+	0.985200i	0.427879	+	0.903836i	$0.359261\pi$
$61$	−4.44251	+	7.69466i	−0.568806	+	0.985200i	−0.996684	+	0.0813643i	$0.974072\pi$
$62$	1.70547	+	2.37515i	0.216595	+	0.301644i
$63$		0			0
$64$	6.62598	−	4.48289i	0.828248	−	0.560362i
$65$	−0.589469	+	1.02099i	−0.0731147	+	0.126638i
$66$		0			0
$67$	−0.867859	−	1.50318i	−0.106026	−	0.183642i	0.808131	−	0.589003i	$-0.200479\pi$
$67$	−0.867859	−	1.50318i	−0.106026	−	0.183642i	−0.914157	+	0.405361i	$0.867146\pi$
$68$	−12.0090	+	10.5726i	−1.45630	+	1.28211i
$69$		0			0
$70$	0.759395	+	0.592446i	0.0907651	+	0.0708109i
$71$		−	8.97302i		−	1.06490i	−0.846461	−	0.532451i	$-0.821271\pi$
$71$		−	8.97302i		−	1.06490i	0.846461	−	0.532451i	$-0.178729\pi$
$72$		0			0
$73$	−6.57828	+	3.79797i	−0.769929	+	0.444519i	−0.832849	−	0.553500i	$-0.813292\pi$
$73$	−6.57828	+	3.79797i	−0.769929	+	0.444519i	0.0629201	+	0.998019i	$0.479959\pi$
$74$	−9.62174	−	4.34840i	−1.11850	−	0.505491i
$75$		0			0
$76$	0.442003	+	0.149092i	0.0507012	+	0.0171020i
$77$	−9.10921	+	2.67409i	−1.03809	+	0.304741i
$78$		0			0
$79$	7.51791	+	4.34047i	0.845831	+	0.488341i	0.859242	−	0.511569i	$-0.170936\pi$
$79$	7.51791	+	4.34047i	0.845831	+	0.488341i	−0.0134112	+	0.999910i	$0.504269\pi$
$80$	−0.130467	+	1.02136i	−0.0145867	+	0.114192i
$81$		0			0
$82$	0.637840	+	6.41283i	0.0704377	+	0.708179i
$83$			3.79017i			0.416025i	0.978126	+	0.208012i	$0.0666994\pi$
$83$			3.79017i			0.416025i	−0.978126	+	0.208012i	$0.933301\pi$
$84$		0			0
$85$		−	2.05930i		−	0.223362i
$86$	−7.63778	+	0.759678i	−0.823603	+	0.0819182i
$87$		0			0
$88$	−7.42745	−	6.91643i	−0.791769	−	0.737293i
$89$	2.25065	+	1.29941i	0.238569	+	0.137738i	0.614519	−	0.788902i	$-0.289350\pi$
$89$	2.25065	+	1.29941i	0.238569	+	0.137738i	−0.375950	+	0.926640i	$0.622684\pi$
$90$		0			0
$91$	2.85749	−	11.7756i	0.299547	−	1.23442i
$92$	12.6066	+	4.25234i	1.31433	+	0.443337i
$93$		0			0
$94$	−1.65819	+	3.66910i	−0.171029	+	0.378438i
$95$	−0.0519946	+	0.0300191i	−0.00533454	+	0.00307990i
$96$		0			0
$97$			14.6024i			1.48265i	0.671146	+	0.741325i	$0.265802\pi$
$97$			14.6024i			1.48265i	−0.671146	+	0.741325i	$0.734198\pi$
$98$	−9.20434	−	3.64419i	−0.929779	−	0.368119i
$99$		0			0
$100$	6.52034	+	7.40623i	0.652034	+	0.740623i
$101$	0.709937	+	1.22965i	0.0706414	+	0.122354i	0.899183	−	0.437574i	$-0.144162\pi$
$101$	0.709937	+	1.22965i	0.0706414	+	0.122354i	−0.828541	+	0.559928i	$0.810829\pi$
$102$		0			0
$103$	4.42816	−	7.66981i	0.436320	−	0.755728i	−0.561082	−	0.827760i	$-0.689615\pi$
$103$	4.42816	−	7.66981i	0.436320	−	0.755728i	0.997402	+	0.0720316i	$0.0229482\pi$
$104$	12.3853	−	3.79611i	1.21447	−	0.372239i
$105$		0			0
$106$	−2.56189	+	1.83955i	−0.248832	+	0.178673i
$107$	6.00175	−	10.3953i	0.580211	−	1.00496i	−0.415243	−	0.909711i	$-0.636303\pi$
$107$	6.00175	−	10.3953i	0.580211	−	1.00496i	0.995454	−	0.0952445i	$-0.0303633\pi$
$108$		0			0
$109$	−10.8275	+	6.25126i	−1.03709	+	0.598762i	−0.919007	−	0.394242i	$-0.871007\pi$
$109$	−10.8275	+	6.25126i	−1.03709	+	0.598762i	−0.118080	+	0.993004i	$0.537674\pi$
$110$	1.29985	−	0.129287i	0.123936	−	0.0123270i
$111$		0			0
$112$	−1.67026	−	10.4504i	−0.157824	−	0.987467i
$113$	−0.143571			−0.0135061			−0.00675303	−	0.999977i	$-0.502150\pi$
$113$	−0.143571			−0.0135061			−0.00675303	+	0.999977i	$0.502150\pi$
$114$		0			0
$115$	−1.48297	+	0.856194i	−0.138288	+	0.0798405i
$116$	−1.10625	−	5.50609i	−0.102713	−	0.511227i
$117$		0			0
$118$	−2.84792	+	2.04494i	−0.262172	+	0.188252i
$119$	5.96184	+	20.3088i	0.546521	+	1.86170i
$120$		0			0
$121$	−0.937751	+	1.62423i	−0.0852501	+	0.147657i
$122$	−5.17478	+	11.4503i	−0.468503	+	1.03666i
$123$		0			0
$124$	2.73251	+	3.10376i	0.245386	+	0.278726i
$125$	−2.55709			−0.228713
$126$		0			0
$127$			18.5252i			1.64385i	0.569597	+	0.821924i	$0.307099\pi$
$127$			18.5252i			1.64385i	−0.569597	+	0.821924i	$0.692901\pi$
$128$	8.69707	−	7.23609i	0.768720	−	0.639586i
$129$		0			0
$130$	−0.686633	+	1.51932i	−0.0602217	+	0.133253i
$131$	−11.3578	−	6.55743i	−0.992336	−	0.572925i	−0.0863640	−	0.996264i	$-0.527525\pi$
$131$	−11.3578	−	6.55743i	−0.992336	−	0.572925i	−0.905972	+	0.423338i	$0.860858\pi$
$132$		0			0
$133$	0.425863	−	0.446577i	0.0369270	−	0.0387232i
$134$	−1.43171	−	1.99390i	−0.123681	−	0.172247i
$135$		0			0
$136$	−15.4200	+	16.5594i	−1.32226	+	1.41995i
$137$	−1.26333	−	2.18816i	−0.107934	−	0.186947i	0.806999	−	0.590552i	$-0.201090\pi$
$137$	−1.26333	−	2.18816i	−0.107934	−	0.186947i	−0.914933	+	0.403606i	$0.867757\pi$
$138$		0			0
$139$		−	16.8020i		−	1.42512i	−0.701609	−	0.712562i	$-0.747535\pi$
$139$		−	16.8020i		−	1.42512i	0.701609	−	0.712562i	$-0.252465\pi$
$140$	1.15160	+	0.727438i	0.0973279	+	0.0614797i
$141$		0			0
$142$	−1.25597	−	12.6275i	−0.105398	−	1.05967i
$143$	−8.21693	−	14.2321i	−0.687134	−	1.19015i
$144$		0			0
$145$	0.625995	+	0.361418i	0.0519860	+	0.0300141i
$146$	−8.72580	+	6.26554i	−0.722153	+	0.518540i
$147$		0			0
$148$	−14.1490	−	4.77260i	−1.16304	−	0.392305i
$149$	20.1564	+	11.6373i	1.65128	+	0.953366i	0.976547	+	0.215303i	$0.0690738\pi$
$149$	20.1564	+	11.6373i	1.65128	+	0.953366i	0.674731	+	0.738064i	$0.264260\pi$
$150$		0			0
$151$	−10.6125	+	6.12714i	−0.863634	+	0.498619i	−0.865227	−	0.501380i	$-0.832826\pi$
$151$	−10.6125	+	6.12714i	−0.863634	+	0.498619i	0.00159368	+	0.999999i	$0.499493\pi$
$152$	0.642886	+	0.147944i	0.0521449	+	0.0119999i
$153$		0			0
$154$	−12.4448	+	5.03820i	−1.00283	+	0.405990i
$155$	−0.532231			−0.0427498
$156$		0			0
$157$	−10.3040	−	17.8471i	−0.822352	−	1.42436i	−0.903926	−	0.427688i	$-0.859328\pi$
$157$	−10.3040	−	17.8471i	−0.822352	−	1.42436i	0.0815741	−	0.996667i	$-0.474005\pi$
$158$	11.1873	+	5.05591i	0.890011	+	0.402227i
$159$		0			0
$160$	−0.0406410	+	1.45559i	−0.00321295	+	0.115075i
$161$	12.1463	−	12.7371i	0.957264	−	1.00383i
$162$		0			0
$163$	7.21136	−	12.4904i	0.564837	−	0.978326i	−0.432228	−	0.901764i	$-0.642272\pi$
$163$	7.21136	−	12.4904i	0.564837	−	0.978326i	0.997065	−	0.0765619i	$-0.0243943\pi$
$164$	1.79523	+	8.93530i	0.140184	+	0.697730i
$165$		0			0
$166$	0.530515	+	5.33379i	0.0411760	+	0.413982i
$167$	7.63662			0.590939			0.295470	−	0.955352i	$-0.404524\pi$
$167$	7.63662			0.590939			0.295470	+	0.955352i	$0.404524\pi$
$168$		0			0
$169$	7.97564			0.613510
$170$	−0.288243	−	2.89799i	−0.0221072	−	0.222265i
$171$		0			0
$172$	−10.6421	+	2.13814i	−0.811452	+	0.163032i
$173$	7.89966	−	13.6826i	0.600600	−	1.04027i	−0.392130	−	0.919910i	$-0.628262\pi$
$173$	7.89966	−	13.6826i	0.600600	−	1.04027i	0.992730	−	0.120360i	$-0.0384050\pi$
$174$		0			0
$175$	12.5249	−	3.67681i	0.946794	−	0.277940i
$176$	−11.4205	−	8.69364i	−0.860855	−	0.655308i
$177$		0			0
$178$	3.34916	+	1.51360i	0.251030	+	0.113449i
$179$	11.4726	+	19.8711i	0.857500	+	1.48523i	0.874306	+	0.485374i	$0.161317\pi$
$179$	11.4726	+	19.8711i	0.857500	+	1.48523i	−0.0168065	+	0.999859i	$0.505350\pi$
$180$		0			0
$181$	15.1773			1.12812			0.564060	−	0.825734i	$-0.309239\pi$
$181$	15.1773			1.12812			0.564060	+	0.825734i	$0.309239\pi$
$182$	2.37302	−	16.9714i	0.175900	−	1.25800i
$183$		0			0
$184$	18.3362	+	4.21961i	1.35176	+	0.311074i
$185$	1.66441	−	0.960948i	0.122370	−	0.0706503i
$186$		0			0
$187$	24.8598	+	14.3528i	1.81793	+	1.04958i
$188$	−1.81995	+	5.39551i	−0.132734	+	0.393508i
$189$		0			0
$190$	−0.0689686	+	0.0495227i	−0.00500351	+	0.00359276i
$191$	−18.5980	−	10.7376i	−1.34571	−	0.776944i	−0.358069	−	0.933695i	$-0.616565\pi$
$191$	−18.5980	−	10.7376i	−1.34571	−	0.776944i	−0.987638	+	0.156751i	$0.949898\pi$
$192$		0			0
$193$	3.58036	+	6.20137i	0.257720	+	0.446384i	0.965631	−	0.259918i	$-0.0836954\pi$
$193$	3.58036	+	6.20137i	0.257720	+	0.446384i	−0.707911	+	0.706302i	$0.750362\pi$
$194$	2.04392	+	20.5495i	0.146745	+	1.47537i
$195$		0			0
$196$	−13.4631	−	3.84002i	−0.961648	−	0.274287i
$197$		−	9.29594i		−	0.662309i	−0.943577	−	0.331154i	$-0.892562\pi$
$197$		−	9.29594i		−	0.662309i	0.943577	−	0.331154i	$-0.107438\pi$
$198$		0			0
$199$	−10.3895	−	17.9951i	−0.736491	−	1.27564i	−0.954066	−	0.299596i	$-0.903148\pi$
$199$	−10.3895	−	17.9951i	−0.736491	−	1.27564i	0.217575	−	0.976043i	$-0.430185\pi$
$200$	10.2125	+	9.50989i	0.722136	+	0.672451i
$201$		0			0
$202$	1.17119	+	1.63107i	0.0824045	+	0.114762i
$203$	−7.21989	−	1.75200i	−0.506737	−	0.122966i
$204$		0			0
$205$	−1.01587	−	0.586511i	−0.0709512	−	0.0409637i
$206$	5.15807	−	11.4133i	0.359380	−	0.795202i
$207$		0			0
$208$	16.8981	−	7.07573i	1.17167	−	0.490614i
$209$		−	0.836905i		−	0.0578899i
$210$		0			0
$211$	5.13459			0.353480			0.176740	−	0.984258i	$-0.443445\pi$
$211$	5.13459			0.353480			0.176740	+	0.984258i	$0.443445\pi$
$212$	−3.34778	+	2.94734i	−0.229926	+	0.202424i
$213$		0			0
$214$	6.99103	−	15.4691i	0.477897	−	1.05745i
$215$	0.698544	−	1.20991i	0.0476403	−	0.0825154i
$216$		0			0
$217$	5.24887	−	1.54085i	0.356316	−	0.104600i
$218$	−14.3622	+	10.3128i	−0.972732	+	0.698468i
$219$		0			0
$220$	1.81114	−	0.363884i	0.122107	−	0.0245330i
$221$	−31.7303	+	18.3195i	−2.13441	+	1.23230i
$222$		0			0
$223$	8.76372			0.586862			0.293431	−	0.955980i	$-0.405203\pi$
$223$	8.76372			0.586862			0.293431	+	0.955980i	$0.405203\pi$
$224$	−3.81326	−	14.4727i	−0.254784	−	0.966998i
$225$		0			0
$226$	−0.202044	+	0.0200959i	−0.0134397	+	0.00133676i
$227$	5.09712	−	2.94282i	0.338308	−	0.195322i	−0.321216	−	0.947006i	$-0.604091\pi$
$227$	5.09712	−	2.94282i	0.338308	−	0.195322i	0.659523	+	0.751684i	$0.270758\pi$
$228$		0			0
$229$	−7.90278	+	13.6880i	−0.522230	+	0.904529i	0.477435	+	0.878667i	$0.341566\pi$
$229$	−7.90278	+	13.6880i	−0.522230	+	0.904529i	−0.999666	+	0.0258624i	$0.991767\pi$
$230$	−1.96710	+	1.41247i	−0.129707	+	0.0931355i
$231$		0			0
$232$	−2.32749	−	7.59371i	−0.152807	−	0.498551i
$233$	0.159081	−	0.275536i	0.0104217	−	0.0180510i	−0.860768	−	0.508998i	$-0.830016\pi$
$233$	0.159081	−	0.275536i	0.0104217	−	0.0180510i	0.871189	+	0.490947i	$0.163349\pi$
$234$		0			0
$235$	−0.366442	−	0.634696i	−0.0239040	−	0.0414030i
$236$	−3.72155	+	3.27641i	−0.242252	+	0.213276i
$237$		0			0
$238$	11.2326	+	27.7455i	0.728099	+	1.79847i
$239$		−	1.46820i		−	0.0949697i	−0.998872	−	0.0474849i	$-0.984879\pi$
$239$		−	1.46820i		−	0.0949697i	0.998872	−	0.0474849i	$-0.0151206\pi$
$240$		0			0
$241$	−12.8350	+	7.41030i	−0.826776	+	0.477339i	−0.852748	−	0.522323i	$-0.825065\pi$
$241$	−12.8350	+	7.41030i	−0.826776	+	0.477339i	0.0259714	+	0.999663i	$0.491732\pi$
$242$	−1.09232	+	2.41699i	−0.0702171	+	0.155370i
$243$		0			0
$244$	−5.67960	+	16.8380i	−0.363599	+	1.07794i
$245$	1.51598	−	0.973995i	0.0968523	−	0.0622263i
$246$		0			0
$247$	0.925087	+	0.534099i	0.0588619	+	0.0339839i
$248$	4.27981	+	3.98535i	0.271768	+	0.253070i
$249$		0			0
$250$	−3.59852	+	0.357920i	−0.227590	+	0.0226368i
$251$		−	10.0773i		−	0.636074i	−0.948078	−	0.318037i	$-0.896976\pi$
$251$		−	10.0773i		−	0.636074i	0.948078	−	0.318037i	$-0.103024\pi$
$252$		0			0
$253$		−	23.8699i		−	1.50069i
$254$	2.59300	+	26.0700i	0.162699	+	1.63578i
$255$		0			0
$256$	11.2263	−	11.4005i	0.701642	−	0.712529i
$257$	15.8763	+	9.16617i	0.990334	+	0.571770i	0.905374	−	0.424615i	$-0.139590\pi$
$257$	15.8763	+	9.16617i	0.990334	+	0.571770i	0.0849601	+	0.996384i	$0.472924\pi$
$258$		0			0
$259$	−13.6324	+	14.2955i	−0.847076	+	0.888278i
$260$	−0.753616	+	2.23420i	−0.0467373	+	0.138559i
$261$		0			0
$262$	−16.9013	−	7.63830i	−1.04417	−	0.471896i
$263$	2.62507	−	1.51558i	0.161869	−	0.0934549i	−0.416877	−	0.908963i	$-0.636876\pi$
$263$	2.62507	−	1.51558i	0.161869	−	0.0934549i	0.578746	+	0.815508i	$0.303542\pi$
$264$		0			0
$265$		−	0.574076i		−	0.0352652i
$266$	0.536796	−	0.688063i	0.0329131	−	0.0421879i
$267$		0			0
$268$	−2.29390	−	2.60555i	−0.140122	−	0.159160i
$269$	−12.7236	−	22.0380i	−0.775774	−	1.34368i	−0.934358	−	0.356335i	$-0.884026\pi$
$269$	−12.7236	−	22.0380i	−0.775774	−	1.34368i	0.158584	−	0.987345i	$-0.449307\pi$
$270$		0			0
$271$	10.4445	−	18.0904i	0.634458	−	1.09891i	−0.352172	−	0.935935i	$-0.614557\pi$
$271$	10.4445	−	18.0904i	0.634458	−	1.09891i	0.986630	−	0.162978i	$-0.0521098\pi$
$272$	−19.3823	+	25.4618i	−1.17522	+	1.54385i
$273$		0			0
$274$	−2.08413	−	2.90250i	−0.125907	−	0.175346i
$275$	8.85173	−	15.3316i	0.533779	−	0.924533i
$276$		0			0
$277$	15.4661	−	8.92934i	0.929266	−	0.536512i	0.0426868	−	0.999089i	$-0.486408\pi$
$277$	15.4661	−	8.92934i	0.929266	−	0.536512i	0.886579	+	0.462576i	$0.153075\pi$
$278$	−2.35180	−	23.6449i	−0.141051	−	1.41813i
$279$		0			0
$280$	1.72243	+	0.862510i	0.102935	+	0.0515449i
$281$	−3.12507			−0.186426			−0.0932132	−	0.995646i	$-0.529714\pi$
$281$	−3.12507			−0.186426			−0.0932132	+	0.995646i	$0.529714\pi$
$282$		0			0
$283$	−13.3128	+	7.68615i	−0.791364	+	0.456894i	−0.840442	−	0.541901i	$-0.817705\pi$
$283$	−13.3128	+	7.68615i	−0.791364	+	0.456894i	0.0490788	+	0.998795i	$0.484371\pi$
$284$	−3.53497	−	17.5944i	−0.209762	−	1.04404i
$285$		0			0
$286$	−13.5555	−	18.8783i	−0.801555	−	1.11630i
$287$	11.7165	+	2.84315i	0.691602	+	0.167826i
$288$		0			0
$289$	23.4993	−	40.7020i	1.38231	−	2.39424i
$290$	0.931531	+	0.420991i	0.0547014	+	0.0247215i
$291$		0			0
$292$	−11.4026	+	10.0387i	−0.667285	+	0.587469i
$293$	23.0311			1.34549			0.672746	−	0.739873i	$-0.265115\pi$
$293$	23.0311			1.34549			0.672746	+	0.739873i	$0.265115\pi$
$294$		0			0
$295$		−	0.638171i		−	0.0371557i
$296$	−20.5795	−	4.73588i	−1.19616	−	0.275267i
$297$		0			0
$298$	29.9944	+	13.5555i	1.73753	+	0.785250i
$299$	26.3850	+	15.2334i	1.52588	+	0.880969i
$300$		0			0
$301$	−3.38624	+	13.9545i	−0.195180	+	0.804325i
$302$	−14.0770	+	10.1080i	−0.810043	+	0.581649i
$303$		0			0
$304$	0.925422	+	0.118212i	0.0530766	+	0.00677992i
$305$	−1.14357	−	1.98072i	−0.0654806	−	0.113416i
$306$		0			0
$307$			4.16830i			0.237898i	0.992900	+	0.118949i	$0.0379524\pi$
$307$			4.16830i			0.237898i	−0.992900	+	0.118949i	$0.962048\pi$
$308$	−16.8080	+	8.83203i	−0.957725	+	0.503252i
$309$		0			0
$310$	−0.748993	+	0.0744972i	−0.0425399	+	0.00423116i
$311$	−0.255482	−	0.442507i	−0.0144870	−	0.0250923i	0.858691	−	0.512494i	$-0.171278\pi$
$311$	−0.255482	−	0.442507i	−0.0144870	−	0.0250923i	−0.873178	+	0.487401i	$0.837945\pi$
$312$		0			0
$313$	−12.1966	−	7.04172i	−0.689393	−	0.398021i	0.113991	−	0.993482i	$-0.463636\pi$
$313$	−12.1966	−	7.04172i	−0.689393	−	0.398021i	−0.803385	+	0.595460i	$0.796970\pi$
$314$	−16.9987	−	23.6734i	−0.959290	−	1.33597i
$315$		0			0
$316$	16.4512	+	5.54914i	0.925451	+	0.312163i
$317$	4.17009	+	2.40760i	0.234216	+	0.135224i	0.612515	−	0.790459i	$-0.290158\pi$
$317$	4.17009	+	2.40760i	0.234216	+	0.135224i	−0.378300	+	0.925683i	$0.623491\pi$
$318$		0			0
$319$	−8.72608	+	5.03800i	−0.488566	+	0.282074i
$320$	0.146548	+	2.05410i	0.00819231	+	0.114828i
$321$		0			0
$322$	15.3103	−	19.6247i	0.853210	−	1.09364i
$323$	−1.86586			−0.103819
$324$		0			0
$325$	11.2981	+	19.5688i	0.626703	+	1.08548i
$326$	8.40002	−	18.5868i	0.465234	−	1.02943i
$327$		0			0
$328$	3.77706	+	12.3231i	0.208553	+	0.680429i
$329$	5.45135	+	5.19849i	0.300543	+	0.286602i
$330$		0			0
$331$	−10.5895	+	18.3415i	−0.582049	+	1.00814i	0.413187	+	0.910646i	$0.364416\pi$
$331$	−10.5895	+	18.3415i	−0.582049	+	1.00814i	−0.995236	+	0.0974930i	$0.968918\pi$
$332$	1.49316	+	7.43182i	0.0819476	+	0.407874i
$333$		0			0
$334$	10.7468	−	1.06891i	0.588038	−	0.0584881i
$335$	0.446800			0.0244113
$336$		0			0
$337$	13.0422			0.710454			0.355227	−	0.934780i	$-0.384404\pi$
$337$	13.0422			0.710454			0.355227	+	0.934780i	$0.384404\pi$
$338$	11.2239	−	1.11636i	0.610498	−	0.0607221i
$339$		0			0
$340$	−0.811271	−	4.03790i	−0.0439973	−	0.218986i
$341$	3.70953	−	6.42509i	0.200882	−	0.347938i
$342$		0			0
$343$	−12.1308	+	13.9944i	−0.655001	+	0.755628i
$344$	−14.6770	+	4.49853i	−0.791331	+	0.242545i
$345$		0			0
$346$	9.20178	−	20.3609i	0.494691	−	1.09461i
$347$	2.51166	+	4.35032i	0.134833	+	0.233537i	0.925534	−	0.378665i	$-0.123617\pi$
$347$	2.51166	+	4.35032i	0.134833	+	0.233537i	−0.790701	+	0.612203i	$0.790284\pi$
$348$		0			0
$349$	13.9823			0.748455			0.374227	−	0.927337i	$-0.377908\pi$
$349$	13.9823			0.748455			0.374227	+	0.927337i	$0.377908\pi$
$350$	17.1113	−	6.92739i	0.914637	−	0.370284i
$351$		0			0
$352$	−17.2886	−	10.6358i	−0.921487	−	0.566888i
$353$	2.00338	−	1.15665i	0.106629	−	0.0615622i	−0.445737	−	0.895164i	$-0.647058\pi$
$353$	2.00338	−	1.15665i	0.106629	−	0.0615622i	0.552366	+	0.833602i	$0.313725\pi$
$354$		0			0
$355$	2.00034	+	1.15489i	0.106167	+	0.0612954i
$356$	4.92503	+	1.66126i	0.261026	+	0.0880464i
$357$		0			0
$358$	18.9264	+	26.3581i	1.00029	+	1.39307i
$359$	8.33838	+	4.81417i	0.440083	+	0.254082i	0.703633	−	0.710564i	$-0.251560\pi$
$359$	8.33838	+	4.81417i	0.440083	+	0.254082i	−0.263550	+	0.964646i	$0.584893\pi$
$360$		0			0
$361$	−9.47280	−	16.4074i	−0.498568	−	0.863546i
$362$	21.3586	−	2.12439i	1.12258	−	0.111655i
$363$		0			0
$364$	0.963971	−	24.2155i	0.0505258	−	1.26924i
$365$		−	1.95531i		−	0.102346i
$366$		0			0
$367$	−3.79729	−	6.57711i	−0.198217	−	0.343322i	0.749733	−	0.661740i	$-0.230182\pi$
$367$	−3.79729	−	6.57711i	−0.198217	−	0.343322i	−0.947950	+	0.318418i	$0.896848\pi$
$368$	26.3945	+	3.37160i	1.37591	+	0.175757i
$369$		0			0
$370$	2.20777	−	1.58528i	0.114776	−	0.0824149i
$371$	1.66200	+	5.66154i	0.0862866	+	0.293932i
$372$		0			0
$373$	17.6547	+	10.1929i	0.914124	+	0.527769i	0.881756	−	0.471707i	$-0.156362\pi$
$373$	17.6547	+	10.1929i	0.914124	+	0.527769i	0.0323679	+	0.999476i	$0.489695\pi$
$374$	36.9935	+	16.7186i	1.91289	+	0.864500i
$375$		0			0
$376$	−1.80595	+	7.84768i	−0.0931348	+	0.404713i
$377$		−	12.8607i		−	0.662359i
$378$		0			0
$379$	−35.3247			−1.81451			−0.907253	−	0.420584i	$-0.861825\pi$
$379$	−35.3247			−1.81451			−0.907253	+	0.420584i	$0.861825\pi$
$380$	−0.0901257	+	0.0793455i	−0.00462335	+	0.00407034i
$381$		0			0
$382$	−27.6754	−	12.5075i	−1.41600	−	0.639938i
$383$	7.06305	−	12.2336i	0.360905	−	0.625106i	−0.627205	−	0.778854i	$-0.715801\pi$
$383$	7.06305	−	12.2336i	0.360905	−	0.625106i	0.988110	+	0.153748i	$0.0491345\pi$
$384$		0			0
$385$	0.576293	−	2.37487i	0.0293706	−	0.121035i
$386$	5.90655	+	8.22585i	0.300636	+	0.418685i
$387$		0			0
$388$	5.75270	+	28.6326i	0.292049	+	1.45360i
$389$	1.66609	−	0.961919i	0.0844743	−	0.0487712i	−0.457168	−	0.889380i	$-0.651136\pi$
$389$	1.66609	−	0.961919i	0.0844743	−	0.0487712i	0.541642	+	0.840609i	$0.317803\pi$
$390$		0			0
$391$	−53.2175			−2.69132
$392$	−19.4837	−	3.51950i	−0.984074	−	0.177761i
$393$		0			0
$394$	−1.30117	−	13.0819i	−0.0655518	−	0.659057i
$395$	−1.93522	+	1.11730i	−0.0973715	+	0.0562175i
$396$		0			0
$397$	−5.33766	+	9.24510i	−0.267890	+	0.463998i	−0.968317	−	0.249726i	$-0.919660\pi$
$397$	−5.33766	+	9.24510i	−0.267890	+	0.463998i	0.700427	+	0.713724i	$0.252993\pi$
$398$	−17.1396	−	23.8697i	−0.859131	−	1.19648i
$399$		0			0
$400$	15.7029	+	11.9535i	0.785146	+	0.597676i
$401$	−6.90465	+	11.9592i	−0.344802	+	0.597214i	−0.985318	−	0.170731i	$-0.945387\pi$
$401$	−6.90465	+	11.9592i	−0.344802	+	0.597214i	0.640516	+	0.767945i	$0.278720\pi$
$402$		0			0
$403$	4.73472	+	8.20078i	0.235853	+	0.408510i
$404$	1.87648	+	2.13143i	0.0933584	+	0.106043i
$405$		0			0
$406$	−10.4056	−	1.45496i	−0.516420	−	0.0722083i
$407$			26.7903i			1.32795i
$408$		0			0
$409$	19.5725	−	11.3002i	0.967797	−	0.558758i	0.0692334	−	0.997600i	$-0.477945\pi$
$409$	19.5725	−	11.3002i	0.967797	−	0.558758i	0.898564	+	0.438842i	$0.144611\pi$
$410$	−1.51169	−	0.683187i	−0.0746572	−	0.0337402i
$411$		0			0
$412$	5.66126	−	16.7836i	0.278910	−	0.826867i
$413$	1.84756	+	6.29364i	0.0909124	+	0.309690i
$414$		0			0
$415$	−0.844933	−	0.487823i	−0.0414762	−	0.0239463i
$416$	22.7897	−	12.3227i	1.11736	−	0.604170i
$417$		0			0
$418$	−0.117143	−	1.17775i	−0.00572964	−	0.0576057i
$419$		−	18.9813i		−	0.927299i	−0.886019	−	0.463650i	$-0.846540\pi$
$419$		−	18.9813i		−	0.927299i	0.886019	−	0.463650i	$-0.153460\pi$
$420$		0			0
$421$		−	18.7332i		−	0.912999i	−0.889724	−	0.456499i	$-0.849103\pi$
$421$		−	18.7332i		−	0.912999i	0.889724	−	0.456499i	$-0.150897\pi$
$422$	7.22575	−	0.718696i	0.351744	−	0.0349856i
$423$		0			0
$424$	−4.29868	+	4.61630i	−0.208763	+	0.224187i
$425$	−34.1816	−	19.7347i	−1.65805	−	0.957276i
$426$		0			0
$427$	17.0122	+	16.2231i	0.823280	+	0.785093i
$428$	7.67303	−	22.7478i	0.370890	−	1.09955i
$429$		0			0
$430$	0.813686	−	1.80045i	0.0392394	−	0.0868254i
$431$	−22.2380	+	12.8391i	−1.07117	+	0.618439i	−0.928500	−	0.371331i	$-0.878901\pi$
$431$	−22.2380	+	12.8391i	−1.07117	+	0.618439i	−0.142668	+	0.989771i	$0.545568\pi$
$432$		0			0
$433$		−	9.18476i		−	0.441392i	−0.975343	−	0.220696i	$-0.929167\pi$
$433$		−	9.18476i		−	0.441392i	0.975343	−	0.220696i	$-0.0708328\pi$
$434$	7.17090	−	2.90309i	0.344214	−	0.139353i
$435$		0			0
$436$	−18.7680	+	16.5231i	−0.898825	+	0.791314i
$437$	0.775770	+	1.34367i	0.0371101	+	0.0642766i
$438$		0			0
$439$	9.86253	−	17.0824i	0.470713	−	0.815298i	−0.528726	−	0.848792i	$-0.677330\pi$
$439$	9.86253	−	17.0824i	0.470713	−	0.815298i	0.999439	+	0.0334941i	$0.0106635\pi$
$440$	2.49783	−	0.765591i	0.119079	−	0.0364981i
$441$		0			0
$442$	−42.0888	+	30.2218i	−2.00196	+	1.43750i
$443$	−13.0143	+	22.5415i	−0.618330	+	1.07098i	0.371460	+	0.928449i	$0.378857\pi$
$443$	−13.0143	+	22.5415i	−0.618330	+	1.07098i	−0.989790	+	0.142531i	$0.954476\pi$
$444$		0			0
$445$	−0.579351	+	0.334489i	−0.0274639	+	0.0158563i
$446$	12.3329	−	1.22667i	0.583980	−	0.0580845i
$447$		0			0
$448$	−7.39204	−	19.8332i	−0.349241	−	0.937033i
$449$	−10.8554			−0.512297			−0.256148	−	0.966637i	$-0.582454\pi$
$449$	−10.8554			−0.512297			−0.256148	+	0.966637i	$0.582454\pi$
$450$		0			0
$451$	14.1607	−	8.17569i	0.666802	−	0.384978i
$452$	−0.281517	+	0.0565607i	−0.0132414	+	0.00266039i
$453$		0			0
$454$	6.76111	−	4.85480i	0.317315	−	0.227847i
$455$	2.25732	+	2.15262i	0.105825	+	0.100916i
$456$		0			0
$457$	−15.0321	+	26.0363i	−0.703171	+	1.21793i	0.264177	+	0.964474i	$0.414900\pi$
$457$	−15.0321	+	26.0363i	−0.703171	+	1.21793i	−0.967348	+	0.253453i	$0.918434\pi$
$458$	−9.20541	+	20.3689i	−0.430140	+	0.951776i
$459$		0			0
$460$	−2.57053	+	2.26306i	−0.119852	+	0.105516i
$461$	9.23630			0.430177			0.215089	−	0.976595i	$-0.430996\pi$
$461$	9.23630			0.430177			0.215089	+	0.976595i	$0.430996\pi$
$462$		0			0
$463$			17.3618i			0.806869i	0.915008	+	0.403435i	$0.132184\pi$
$463$			17.3618i			0.806869i	−0.915008	+	0.403435i	$0.867816\pi$
$464$	−4.33830	−	10.3606i	−0.201401	−	0.480979i
$465$		0			0
$466$	0.185302	−	0.410020i	0.00858396	−	0.0189938i
$467$	−18.8961	−	10.9097i	−0.874408	−	0.504840i	−0.00559766	−	0.999984i	$-0.501782\pi$
$467$	−18.8961	−	10.9097i	−0.874408	−	0.504840i	−0.868811	+	0.495144i	$0.835115\pi$
$468$		0			0
$469$	−4.40634	+	1.29352i	−0.203466	+	0.0597293i
$470$	−0.604522	−	0.841897i	−0.0278845	−	0.0388338i
$471$		0			0
$472$	−4.77862	+	5.13170i	−0.219954	+	0.236206i
$473$	9.73738	+	16.8656i	0.447725	+	0.775483i
$474$		0			0
$475$			1.15072i			0.0527987i
$476$	19.6908	+	37.4731i	0.902527	+	1.71758i
$477$		0			0
$478$	−0.205506	−	2.06615i	−0.00939961	−	0.0945034i
$479$	−10.2056	−	17.6766i	−0.466306	−	0.807665i	0.532954	−	0.846144i	$-0.321082\pi$
$479$	−10.2056	−	17.6766i	−0.466306	−	0.807665i	−0.999259	+	0.0384791i	$0.987749\pi$
$480$		0			0
$481$	−29.6131	−	17.0972i	−1.35024	−	0.779563i
$482$	−17.0251	+	12.2248i	−0.775472	+	0.556826i
$483$		0			0
$484$	−1.19888	+	3.55425i	−0.0544946	+	0.161557i
$485$	−3.25528	−	1.87944i	−0.147815	−	0.0853409i
$486$		0			0
$487$	7.32382	−	4.22841i	0.331874	−	0.191608i	−0.324799	−	0.945783i	$-0.605297\pi$
$487$	7.32382	−	4.22841i	0.331874	−	0.191608i	0.656673	+	0.754176i	$0.271963\pi$
$488$	−5.63590	+	24.4905i	−0.255125	+	1.10863i
$489$		0			0
$490$	1.99706	−	1.58287i	0.0902179	−	0.0715067i
$491$	−37.4822			−1.69155			−0.845774	−	0.533541i	$-0.820861\pi$
$491$	−37.4822			−1.69155			−0.845774	+	0.533541i	$0.820861\pi$
$492$		0			0
$493$	11.2321	+	19.4546i	0.505869	+	0.876191i
$494$	1.37661	+	0.622136i	0.0619364	+	0.0279912i
$495$		0			0
$496$	6.58069	+	5.00941i	0.295481	+	0.224929i
$497$	−23.0708	−	5.59843i	−1.03487	−	0.251124i
$498$		0			0
$499$	−6.23338	+	10.7965i	−0.279045	+	0.483319i	−0.971148	−	0.238479i	$-0.923351\pi$
$499$	−6.23338	+	10.7965i	−0.279045	+	0.483319i	0.692103	+	0.721799i	$0.256684\pi$
$500$	−5.01399	+	1.00738i	−0.224232	+	0.0450514i
$501$		0			0
$502$	−1.41054	−	14.1815i	−0.0629553	−	0.632951i
$503$	−13.8883			−0.619250			−0.309625	−	0.950859i	$-0.600203\pi$
$503$	−13.8883			−0.619250			−0.309625	+	0.950859i	$0.600203\pi$
$504$		0			0
$505$	−0.365497			−0.0162644
$506$	−3.34111	−	33.5914i	−0.148530	−	1.49332i
$507$		0			0
$508$	7.29811	+	36.3246i	0.323801	+	1.61164i
$509$	−19.5215	+	33.8121i	−0.865273	+	1.49870i	0.00150245	+	0.999999i	$0.499522\pi$
$509$	−19.5215	+	33.8121i	−0.865273	+	1.49870i	−0.866776	+	0.498698i	$0.833812\pi$
$510$		0			0
$511$	5.66078	+	19.2833i	0.250418	+	0.853041i
$512$	14.2027	−	17.6149i	0.627675	−	0.778476i
$513$		0			0
$514$	23.6252	+	10.6770i	1.04206	+	0.470944i
$515$	1.13988	+	1.97432i	0.0502289	+	0.0869990i
$516$		0			0
$517$	10.2161			0.449302
$518$	−17.1835	+	22.0257i	−0.755000	+	0.967755i
$519$		0			0
$520$	−0.747817	+	3.24961i	−0.0327939	+	0.142505i
$521$	−12.2354	+	7.06409i	−0.536041	+	0.309483i	−0.743473	−	0.668766i	$-0.766823\pi$
$521$	−12.2354	+	7.06409i	−0.536041	+	0.309483i	0.207432	+	0.978249i	$0.433489\pi$
$522$		0			0
$523$	9.63976	+	5.56552i	0.421517	+	0.243363i	0.695726	−	0.718307i	$-0.255083\pi$
$523$	9.63976	+	5.56552i	0.421517	+	0.243363i	−0.274209	+	0.961670i	$0.588416\pi$
$524$	−24.8539	−	8.38345i	−1.08575	−	0.366233i
$525$		0			0
$526$	3.48204	−	2.50027i	0.151824	−	0.109017i
$527$	−14.3246	−	8.27032i	−0.623990	−	0.360261i
$528$		0			0
$529$	10.6262	+	18.4052i	0.462010	+	0.800224i
$530$	−0.0803543	−	0.807880i	−0.00349037	−	0.0350921i
$531$		0			0
$532$	0.659108	−	1.04343i	0.0285760	−	0.0452383i
$533$			20.8704i			0.903996i
$534$		0			0
$535$	1.54494	+	2.67591i	0.0667936	+	0.115690i
$536$	−3.59283	−	3.34564i	−0.155187	−	0.144509i
$537$		0			0
$538$	−20.9903	−	29.2325i	−0.904955	−	1.26030i
$539$	1.19205	+	25.0894i	0.0513451	+	1.08068i
$540$		0			0
$541$	−11.0648	−	6.38829i	−0.475715	−	0.274654i	0.242914	−	0.970048i	$-0.421897\pi$
$541$	−11.0648	−	6.38829i	−0.475715	−	0.274654i	−0.718629	+	0.695394i	$0.755230\pi$
$542$	12.1661	−	26.9200i	0.522578	−	1.15631i
$543$		0			0
$544$	−23.7122	+	38.5446i	−1.01665	+	1.65259i
$545$		−	3.21833i		−	0.137858i
$546$		0			0
$547$	−20.6852			−0.884437			−0.442218	−	0.896907i	$-0.645808\pi$
$547$	−20.6852			−0.884437			−0.442218	+	0.896907i	$0.645808\pi$
$548$	−3.33920	−	3.79288i	−0.142644	−	0.162024i
$549$		0			0
$550$	10.3108	−	22.8147i	0.439653	−	0.972824i
$551$	0.327469	−	0.567193i	0.0139507	−	0.0241632i
$552$		0			0
$553$	15.8505	−	16.6214i	0.674031	−	0.706816i
$554$	20.5151	−	14.7308i	0.871602	−	0.625852i
$555$		0			0
$556$	−6.61922	−	32.9456i	−0.280718	−	1.39720i
$557$	−4.75011	+	2.74248i	−0.201268	+	0.116202i	−0.597247	−	0.802057i	$-0.703739\pi$
$557$	−4.75011	+	2.74248i	−0.201268	+	0.116202i	0.395979	+	0.918260i	$0.370405\pi$
$558$		0			0
$559$	−24.8569			−1.05134
$560$	2.54465	+	0.972694i	0.107531	+	0.0411038i
$561$		0			0
$562$	−4.39782	+	0.437421i	−0.185511	+	0.0184515i
$563$	−35.0039	+	20.2095i	−1.47524	+	0.851730i	−0.999610	−	0.0279158i	$-0.991113\pi$
$563$	−35.0039	+	20.2095i	−1.47524	+	0.851730i	−0.475629	+	0.879646i	$0.657780\pi$
$564$		0			0
$565$	0.0184787	−	0.0320060i	0.000777405	−	0.00134650i
$566$	−17.6589	+	12.6799i	−0.742257	+	0.532976i
$567$		0			0
$568$	−7.43737	−	24.2653i	−0.312065	−	1.01815i
$569$	8.93137	−	15.4696i	0.374422	−	0.648519i	−0.615818	−	0.787888i	$-0.711174\pi$
$569$	8.93137	−	15.4696i	0.374422	−	0.648519i	0.990240	+	0.139370i	$0.0445077\pi$
$570$		0			0
$571$	4.38717	+	7.59881i	0.183597	+	0.318000i	0.943103	−	0.332501i	$-0.107892\pi$
$571$	4.38717	+	7.59881i	0.183597	+	0.318000i	−0.759506	+	0.650501i	$0.774559\pi$
$572$	−21.7187	−	24.6695i	−0.908105	−	1.03148i
$573$		0			0
$574$	16.8862	+	2.36111i	0.704816	+	0.0985509i
$575$			32.8205i			1.36871i
$576$		0			0
$577$	−3.76090	+	2.17135i	−0.156568	+	0.0903947i	−0.576237	−	0.817283i	$-0.695480\pi$
$577$	−3.76090	+	2.17135i	−0.156568	+	0.0903947i	0.419669	+	0.907677i	$0.362146\pi$
$578$	27.3728	−	60.5680i	1.13856	−	2.51930i
$579$		0			0
$580$	1.36984	+	0.462061i	0.0568796	+	0.0191860i
$581$	9.74502	+	2.36475i	0.404292	+	0.0981065i
$582$		0			0
$583$	6.93024	+	4.00118i	0.287021	+	0.165712i
$584$	−14.6414	+	15.7231i	−0.605864	+	0.650629i
$585$		0			0
$586$	32.4110	−	3.22370i	1.33889	−	0.133170i
$587$			10.5208i			0.434239i	0.976145	+	0.217119i	$0.0696661\pi$
$587$			10.5208i			0.434239i	−0.976145	+	0.217119i	$0.930334\pi$
$588$		0			0
$589$			0.482238i			0.0198703i
$590$	−0.0893257	−	0.898078i	−0.00367748	−	0.0369733i
$591$		0			0
$592$	−29.6239	−	3.78411i	−1.21753	−	0.155526i
$593$	13.0551	+	7.53735i	0.536107	+	0.309522i	0.743500	−	0.668736i	$-0.233164\pi$
$593$	13.0551	+	7.53735i	0.536107	+	0.309522i	−0.207392	+	0.978258i	$0.566498\pi$
$594$		0			0
$595$	−5.29473	−	1.28483i	−0.217063	−	0.0526730i
$596$	44.1076	+	14.8779i	1.80672	+	0.609423i
$597$		0			0
$598$	39.2630	+	17.7443i	1.60558	+	0.725619i
$599$	6.10386	−	3.52407i	0.249397	−	0.143989i	−0.370091	−	0.928995i	$-0.620674\pi$
$599$	6.10386	−	3.52407i	0.249397	−	0.143989i	0.619488	+	0.785006i	$0.287340\pi$
$600$		0			0
$601$			0.706153i			0.0288046i	0.999896	+	0.0144023i	$0.00458455\pi$
$601$			0.706153i			0.0288046i	−0.999896	+	0.0144023i	$0.995415\pi$
$602$	−2.81212	+	20.1117i	−0.114613	+	0.819693i
$603$		0			0
$604$	−18.3954	+	16.1950i	−0.748497	+	0.658967i
$605$	−0.241391	−	0.418101i	−0.00981394	−	0.0169982i
$606$		0			0
$607$	3.09824	−	5.36632i	0.125754	−	0.217812i	−0.796273	−	0.604937i	$-0.793198\pi$
$607$	3.09824	−	5.36632i	0.125754	−	0.217812i	0.922027	+	0.387125i	$0.126532\pi$
$608$	1.31886	+	0.0368234i	0.0534870	+	0.00149339i
$609$		0			0
$610$	−1.88655	−	2.62734i	−0.0763844	−	0.106378i
$611$	−6.51972	+	11.2925i	−0.263760	+	0.456845i
$612$		0			0
$613$	−9.94156	+	5.73976i	−0.401536	+	0.231827i	−0.687146	−	0.726519i	$-0.741137\pi$
$613$	−9.94156	+	5.73976i	−0.401536	+	0.231827i	0.285611	+	0.958346i	$0.407804\pi$
$614$	0.583443	+	5.86593i	0.0235459	+	0.236729i
$615$		0			0
$616$	−22.4172	+	14.7817i	−0.903214	+	0.595571i
$617$	48.1839			1.93981			0.969905	−	0.243485i	$-0.0782908\pi$
$617$	48.1839			1.93981			0.969905	+	0.243485i	$0.0782908\pi$
$618$		0			0
$619$	10.6872	−	6.17027i	0.429556	−	0.248004i	−0.269602	−	0.962972i	$-0.586892\pi$
$619$	10.6872	−	6.17027i	0.429556	−	0.248004i	0.699157	+	0.714968i	$0.253559\pi$
$620$	−1.04361	+	0.209675i	−0.0419123	+	0.00842076i
$621$		0			0
$622$	−0.421470	−	0.586966i	−0.0168994	−	0.0235352i
$623$	4.74519	−	4.97600i	0.190112	−	0.199359i
$624$		0			0
$625$	−12.0052	+	20.7937i	−0.480209	+	0.831747i
$626$	−18.1496	−	8.20242i	−0.725402	−	0.327835i
$627$		0			0
$628$	−27.2353	−	30.9356i	−1.08681	−	1.23446i
$629$	59.7285			2.38153
$630$		0			0
$631$			2.33444i			0.0929326i	0.998920	+	0.0464663i	$0.0147960\pi$
$631$			2.33444i			0.0929326i	−0.998920	+	0.0464663i	$0.985204\pi$
$632$	23.9280	+	5.50643i	0.951804	+	0.219034i
$633$		0			0
$634$	6.20543	+	2.80445i	0.246449	+	0.111379i
$635$	−4.12979	−	2.38433i	−0.163886	−	0.0946194i
$636$		0			0
$637$	−28.4937	−	14.6940i	−1.12896	−	0.582197i
$638$	−11.5748	+	8.31123i	−0.458249	+	0.329045i
$639$		0			0
$640$	0.493748	+	2.87016i	0.0195171	+	0.113453i
$641$	−22.0146	−	38.1304i	−0.869525	−	1.50606i	−0.862483	−	0.506086i	$-0.831092\pi$
$641$	−22.0146	−	38.1304i	−0.869525	−	1.50606i	−0.00704191	−	0.999975i	$-0.502242\pi$
$642$		0			0
$643$		−	0.391635i		−	0.0154446i	−0.999970	−	0.00772228i	$-0.997542\pi$
$643$		−	0.391635i		−	0.0154446i	0.999970	−	0.00772228i	$-0.00245810\pi$
$644$	18.7988	−	29.7602i	0.740778	−	1.17272i
$645$		0			0
$646$	−2.62577	+	0.261168i	−0.103310	+	0.0102755i
$647$	−13.1914	−	22.8482i	−0.518608	−	0.898256i	−0.999766	−	0.0216222i	$-0.993117\pi$
$647$	−13.1914	−	22.8482i	−0.518608	−	0.898256i	0.481158	−	0.876634i	$-0.340216\pi$
$648$		0			0
$649$	7.70400	+	4.44790i	0.302408	+	0.174596i
$650$	18.6385	+	25.9572i	0.731061	+	1.01812i
$651$		0			0
$652$	9.21947	−	27.3324i	0.361062	−	1.07042i
$653$	−33.2271	−	19.1837i	−1.30028	−	0.750715i	−0.319825	−	0.947477i	$-0.603624\pi$
$653$	−33.2271	−	19.1837i	−1.30028	−	0.750715i	−0.980451	+	0.196762i	$0.936957\pi$
$654$		0			0
$655$	2.92367	−	1.68798i	0.114237	−	0.0659548i
$656$	7.04022	+	16.8132i	0.274874	+	0.656447i
$657$		0			0
$658$	8.39916	+	6.55265i	0.327433	+	0.255449i
$659$	27.8445			1.08467			0.542334	−	0.840163i	$-0.317541\pi$
$659$	27.8445			1.08467			0.542334	+	0.840163i	$0.317541\pi$
$660$		0			0
$661$	−10.0199	−	17.3549i	−0.389728	−	0.675029i	0.602685	−	0.797979i	$-0.294098\pi$
$661$	−10.0199	−	17.3549i	−0.389728	−	0.675029i	−0.992413	+	0.122951i	$0.960764\pi$
$662$	−12.3349	+	27.2936i	−0.479411	+	1.06080i
$663$		0			0
$664$	3.14152	+	10.2496i	0.121914	+	0.397761i
$665$	0.0447427	+	0.152415i	0.00173505	+	0.00591038i
$666$		0			0
$667$	9.33996	−	16.1773i	0.361645	−	0.626387i
$668$	14.9740	−	3.00849i	0.579362	−	0.116402i
$669$		0			0
$670$	0.628767	−	0.0625392i	0.0242914	−	0.00241610i
$671$	31.8817			1.23078
$672$		0			0
$673$	−2.90485			−0.111974			−0.0559868	−	0.998432i	$-0.517830\pi$
$673$	−2.90485			−0.111974			−0.0559868	+	0.998432i	$0.517830\pi$
$674$	18.3539	−	1.82554i	0.706966	−	0.0703170i
$675$		0			0
$676$	15.6388	−	3.14204i	0.601491	−	0.120848i
$677$	14.6961	−	25.4545i	0.564819	−	0.978295i	−0.432248	−	0.901755i	$-0.642279\pi$
$677$	14.6961	−	25.4545i	0.564819	−	0.978295i	0.997067	−	0.0765400i	$-0.0243873\pi$
$678$		0			0
$679$	37.5448	+	9.11071i	1.44084	+	0.349637i
$680$	−1.70687	−	5.56886i	−0.0654554	−	0.213556i
$681$		0			0
$682$	4.32098	−	9.56107i	0.165459	−	0.366112i
$683$	0.120445	+	0.208616i	0.00460868	+	0.00798247i	0.868321	−	0.496003i	$-0.165200\pi$
$683$	0.120445	+	0.208616i	0.00460868	+	0.00798247i	−0.863712	+	0.503986i	$0.831866\pi$
$684$		0			0
$685$	0.650401			0.0248506
$686$	−15.1125	+	21.3919i	−0.576997	+	0.816747i
$687$		0			0
$688$	−20.0248	+	8.38501i	−0.763440	+	0.319676i
$689$	−8.84553	+	5.10697i	−0.336988	+	0.194560i
$690$		0			0
$691$	−26.5759	−	15.3436i	−1.01099	−	0.583698i	−0.0995117	−	0.995036i	$-0.531728\pi$
$691$	−26.5759	−	15.3436i	−1.01099	−	0.583698i	−0.911483	+	0.411339i	$0.865061\pi$
$692$	10.0994	−	29.9412i	0.383923	−	1.13819i
$693$		0			0
$694$	4.14350	+	5.77052i	0.157285	+	0.219046i
$695$	3.74563	+	2.16254i	0.142080	+	0.0820297i
$696$		0			0
$697$	−18.2275	−	31.5710i	−0.690417	−	1.19584i
$698$	19.6768	−	1.95712i	0.744780	−	0.0740781i
$699$		0			0
$700$	23.1106	−	12.1438i	0.873497	−	0.458992i
$701$		−	1.90784i		−	0.0720581i	−0.999351	−	0.0360290i	$-0.988529\pi$
$701$		−	1.90784i		−	0.0720581i	0.999351	−	0.0360290i	$-0.0114709\pi$
$702$		0			0
$703$	−0.870684	−	1.50807i	−0.0328385	−	0.0568779i
$704$	−25.8185	−	12.5475i	−0.973070	−	0.472900i
$705$		0			0
$706$	2.65739	−	1.90813i	0.100012	−	0.0718136i
$707$	3.60453	−	1.05814i	0.135562	−	0.0397956i
$708$		0			0
$709$	29.0031	+	16.7450i	1.08923	+	0.628870i	0.933373	−	0.358909i	$-0.116851\pi$
$709$	29.0031	+	16.7450i	1.08923	+	0.628870i	0.155862	+	0.987779i	$0.450184\pi$
$710$	2.97666	+	1.34526i	0.111712	+	0.0504866i
$711$		0			0
$712$	7.16337	+	1.64847i	0.268459	+	0.0617792i
$713$			13.7542i			0.515099i
$714$		0			0
$715$	4.23032			0.158205
$716$	30.3239	+	34.4438i	1.13326	+	1.28723i
$717$		0			0
$718$	12.4082	+	5.60769i	0.463070	+	0.209277i
$719$	−0.0121575	+	0.0210575i	−0.000453399	+	0.000785311i	−0.866252	−	0.499607i	$-0.833478\pi$
$719$	−0.0121575	+	0.0210575i	−0.000453399	+	0.000785311i	0.865799	+	0.500393i	$0.166811\pi$
$720$		0			0
$721$	−16.9573	−	16.1707i	−0.631522	−	0.602230i
$722$	−15.6273	−	21.7637i	−0.581590	−	0.809960i
$723$		0			0
$724$	29.7599	−	5.97918i	1.10602	−	0.222214i
$725$	11.9981	−	6.92711i	0.445599	−	0.257267i
$726$		0			0
$727$	16.6521			0.617593			0.308797	−	0.951128i	$-0.400074\pi$
$727$	16.6521			0.617593			0.308797	+	0.951128i	$0.400074\pi$
$728$	−2.03291	−	34.2126i	−0.0753445	−	1.26800i
$729$		0			0
$730$	−0.273687	−	2.75165i	−0.0101296	−	0.101843i
$731$	37.6016	−	21.7093i	1.39074	−	0.802947i
$732$		0			0
$733$	13.1766	−	22.8226i	0.486691	−	0.842973i	−0.513192	−	0.858274i	$-0.671537\pi$
$733$	13.1766	−	22.8226i	0.486691	−	0.842973i	0.999883	+	0.0153008i	$0.00487059\pi$
$734$	−6.26442	−	8.72425i	−0.231224	−	0.322018i
$735$		0			0
$736$	37.6162	+	1.05027i	1.38655	+	0.0387133i
$737$	−3.11409	+	5.39376i	−0.114709	+	0.198682i
$738$		0			0
$739$	2.67874	+	4.63971i	0.0985390	+	0.170675i	0.911080	−	0.412229i	$-0.135250\pi$
$739$	2.67874	+	4.63971i	0.0985390	+	0.170675i	−0.812541	+	0.582904i	$0.801916\pi$
$740$	2.88503	−	2.53994i	0.106056	−	0.0933702i
$741$		0			0
$742$	3.13133	+	7.73468i	0.114955	+	0.283949i
$743$		−	33.1321i		−	1.21550i	−0.794129	−	0.607749i	$-0.792073\pi$
$743$		−	33.1321i		−	1.21550i	0.794129	−	0.607749i	$-0.207927\pi$
$744$		0			0
$745$	−5.18856	+	2.99562i	−0.190094	+	0.109751i
$746$	26.2716	+	11.8730i	0.961871	+	0.434703i
$747$		0			0
$748$	54.3999	+	18.3496i	1.98906	+	0.670928i
$749$	−22.9832	−	21.9171i	−0.839788	−	0.800835i
$750$		0			0
$751$	−13.6288	−	7.86861i	−0.497323	−	0.287130i	0.230284	−	0.973123i	$-0.426034\pi$
$751$	−13.6288	−	7.86861i	−0.497323	−	0.287130i	−0.727607	+	0.685994i	$0.759368\pi$
$752$	−1.44301	+	11.2966i	−0.0526211	+	0.411944i
$753$		0			0
$754$	−1.80013	−	18.0984i	−0.0655568	−	0.659106i
$755$		−	3.15443i		−	0.114802i
$756$		0			0
$757$		−	17.9229i		−	0.651418i	−0.945470	−	0.325709i	$-0.894397\pi$
$757$		−	17.9229i		−	0.651418i	0.945470	−	0.325709i	$-0.105603\pi$
$758$	−49.7113	+	4.94445i	−1.80560	+	0.179590i
$759$		0			0
$760$	−0.115725	+	0.124276i	−0.00419779	+	0.00450795i
$761$	−15.7934	−	9.11832i	−0.572510	−	0.330539i	0.185641	−	0.982618i	$-0.440564\pi$
$761$	−15.7934	−	9.11832i	−0.572510	−	0.330539i	−0.758151	+	0.652079i	$0.773897\pi$
$762$		0			0
$763$	9.31735	+	31.7392i	0.337311	+	1.14904i
$764$	−40.6975	−	13.7276i	−1.47238	−	0.496648i
$765$		0			0
$766$	8.22727	−	18.2046i	0.297263	−	0.657757i
$767$	−9.83312	+	5.67716i	−0.355054	+	0.204990i
$768$		0			0
$769$			41.7710i			1.50630i	0.657847	+	0.753151i	$0.271467\pi$
$769$			41.7710i			1.50630i	−0.657847	+	0.753151i	$0.728533\pi$
$770$	0.478586	−	3.42275i	0.0172470	−	0.123347i
$771$		0			0
$772$	9.46350	+	10.7492i	0.340599	+	0.386874i
$773$	22.1831	+	38.4222i	0.797870	+	1.38195i	0.921001	+	0.389561i	$0.127373\pi$
$773$	22.1831	+	38.4222i	0.797870	+	1.38195i	−0.123131	+	0.992390i	$0.539294\pi$
$774$		0			0
$775$	−5.10050	+	8.83433i	−0.183215	+	0.317338i
$776$	12.1034	+	39.4886i	0.434485	+	1.41756i
$777$		0			0
$778$	2.21000	−	1.58689i	0.0792324	−	0.0568926i
$779$	−0.531419	+	0.920444i	−0.0190400	+	0.0329783i
$780$		0			0
$781$	−27.8838	+	16.0987i	−0.997759	+	0.576057i
$782$	−74.8913	+	7.44893i	−2.67811	+	0.266373i
$783$		0			0
$784$	−27.9114	−	2.22573i	−0.996836	−	0.0794902i
$785$	5.30483			0.189337
$786$		0			0
$787$	25.7940	−	14.8922i	0.919458	−	0.530849i	0.0359959	−	0.999352i	$-0.488540\pi$
$787$	25.7940	−	14.8922i	0.919458	−	0.530849i	0.883462	+	0.468503i	$0.155206\pi$
$788$	−3.66219	−	18.2276i	−0.130460	−	0.649333i
$789$		0			0
$790$	−2.56699	+	1.84322i	−0.0913293	+	0.0655788i
$791$	−0.0895768	+	0.369141i	−0.00318498	+	0.0131251i
$792$		0			0
$793$	−20.3463	+	35.2409i	−0.722520	+	1.25144i
$794$	−6.21748	+	13.7575i	−0.220650	+	0.488234i
$795$		0			0
$796$	−27.4611	−	31.1921i	−0.973334	−	1.10557i
$797$	−34.1552			−1.20984			−0.604920	−	0.796286i	$-0.706795\pi$
$797$	−34.1552			−1.20984			−0.604920	+	0.796286i	$0.706795\pi$
$798$		0			0
$799$		−	22.7765i		−	0.805775i
$800$	23.7714	+	14.6239i	0.840446	+	0.517032i
$801$		0			0
$802$	−8.04275	+	17.7963i	−0.283999	+	0.628408i
$803$	23.6045	+	13.6280i	0.832984	+	0.480923i
$804$		0			0
$805$	1.27614	+	4.34711i	0.0449779	+	0.153216i
$806$	7.81090	+	10.8780i	0.275127	+	0.383160i
$807$		0			0
$808$	2.93905	+	2.73684i	0.103396	+	0.0962817i
$809$	13.4152	+	23.2358i	0.471653	+	0.816928i	0.999474	−	0.0324281i	$-0.0103240\pi$
$809$	13.4152	+	23.2358i	0.471653	+	0.816928i	−0.527821	+	0.849356i	$0.676991\pi$
$810$		0			0
$811$		−	45.1596i		−	1.58577i	−0.609372	−	0.792885i	$-0.708578\pi$
$811$		−	45.1596i		−	1.58577i	0.609372	−	0.792885i	$-0.291422\pi$
$812$	−14.8471	−	0.591034i	−0.521031	−	0.0207412i
$813$		0			0
$814$	3.74988	+	37.7012i	0.131433	+	1.32143i
$815$	1.85631	+	3.21522i	0.0650237	+	0.112624i
$816$		0			0
$817$	−1.09626	−	0.632928i	−0.0383534	−	0.0221433i
$818$	25.9621	−	18.6420i	0.907743	−	0.651802i
$819$		0			0
$820$	−2.22299	−	0.749834i	−0.0776301	−	0.0261853i
$821$	17.5238	+	10.1174i	0.611585	+	0.353099i	0.773586	−	0.633692i	$-0.218461\pi$
$821$	17.5238	+	10.1174i	0.611585	+	0.353099i	−0.162000	+	0.986791i	$0.551795\pi$
$822$		0			0
$823$	40.5392	−	23.4053i	1.41311	−	0.815858i	0.417428	−	0.908710i	$-0.362932\pi$
$823$	40.5392	−	23.4053i	1.41311	−	0.815858i	0.995680	+	0.0928521i	$0.0295984\pi$
$824$	5.61769	−	24.4114i	0.195702	−	0.850413i
$825$		0			0
$826$	3.48094	+	8.59825i	0.121117	+	0.299171i
$827$	17.0446			0.592700			0.296350	−	0.955079i	$-0.404231\pi$
$827$	17.0446			0.592700			0.296350	+	0.955079i	$0.404231\pi$
$828$		0			0
$829$	6.94700	+	12.0325i	0.241279	+	0.417908i	0.961079	−	0.276274i	$-0.0890997\pi$
$829$	6.94700	+	12.0325i	0.241279	+	0.417908i	−0.719800	+	0.694182i	$0.755766\pi$
$830$	−1.25733	−	0.568231i	−0.0436426	−	0.0197236i
$831$		0			0
$832$	30.3465	−	20.5313i	1.05207	−	0.711794i
$833$	55.9363	−	2.65765i	1.93808	−	0.0920820i
$834$		0			0
$835$	−0.982890	+	1.70242i	−0.0340143	+	0.0589145i
$836$	−0.329703	−	1.64102i	−0.0114030	−	0.0567558i
$837$		0			0
$838$	−2.65685	−	26.7119i	−0.0917792	−	0.922746i
$839$	−34.7647			−1.20021			−0.600105	−	0.799921i	$-0.704875\pi$
$839$	−34.7647			−1.20021			−0.600105	+	0.799921i	$0.704875\pi$
$840$		0			0
$841$	21.1148			0.728097
$842$	−2.62211	−	26.3626i	−0.0903639	−	0.908516i
$843$		0			0
$844$	10.0680	−	2.02280i	0.346554	−	0.0696276i
$845$	−1.02652	+	1.77799i	−0.0353135	+	0.0611648i
$846$		0			0
$847$	3.59104	+	3.42447i	0.123389	+	0.117666i
$848$	−5.40326	+	7.09807i	−0.185549	+	0.243749i
$849$		0			0
$850$	−50.8650	−	22.9877i	−1.74466	−	0.788470i
$851$	−24.8333	−	43.0126i	−0.851275	−	1.47445i
$852$		0			0
$853$	39.5354			1.35367			0.676834	−	0.736136i	$-0.263352\pi$
$853$	39.5354			1.35367			0.676834	+	0.736136i	$0.263352\pi$
$854$	26.2116	+	20.4491i	0.896942	+	0.699754i
$855$		0			0
$856$	7.61399	−	33.0862i	0.260241	−	1.13086i
$857$	17.9608	−	10.3697i	0.613530	−	0.354221i	−0.160816	−	0.986984i	$-0.551413\pi$
$857$	17.9608	−	10.3697i	0.613530	−	0.354221i	0.774346	+	0.632763i	$0.218079\pi$
$858$		0			0
$859$	−41.7159	−	24.0847i	−1.42333	−	0.821759i	−0.426746	−	0.904371i	$-0.640340\pi$
$859$	−41.7159	−	24.0847i	−1.42333	−	0.821759i	−0.996582	+	0.0826128i	$0.973674\pi$
$860$	0.893064	−	2.64761i	0.0304532	−	0.0902828i
$861$		0			0
$862$	−29.4978	+	21.1808i	−1.00470	+	0.721421i
$863$	38.2263	+	22.0700i	1.30124	+	0.751271i	0.980617	−	0.195937i	$-0.0627747\pi$
$863$	38.2263	+	22.0700i	1.30124	+	0.751271i	0.320622	+	0.947207i	$0.396108\pi$
$864$		0			0
$865$	2.03349	+	3.52211i	0.0691408	+	0.119755i
$866$	−1.28561	−	12.9254i	−0.0436866	−	0.439224i
$867$		0			0
$868$	9.68503	−	5.08915i	0.328731	−	0.172737i
$869$		−	31.1493i		−	1.05667i
$870$		0			0
$871$	−3.97472	−	6.88442i	−0.134678	−	0.233270i
$872$	−24.0989	+	25.8795i	−0.816092	+	0.876390i
$873$		0			0
$874$	1.27979	+	1.78232i	0.0432896	+	0.0602880i
$875$	−1.59542	+	6.57462i	−0.0539349	+	0.222263i
$876$		0			0
$877$	−1.21231	−	0.699930i	−0.0409369	−	0.0236350i	0.479392	−	0.877601i	$-0.340857\pi$
$877$	−1.21231	−	0.699930i	−0.0409369	−	0.0236350i	−0.520329	+	0.853966i	$0.674191\pi$
$878$	11.4882	−	25.4200i	0.387707	−	0.857884i
$879$		0			0
$880$	3.40796	−	1.42702i	0.114882	−	0.0481048i
$881$		−	0.164680i		−	0.00554821i	−0.999996	−	0.00277410i	$-0.999117\pi$
$881$		−	0.164680i		−	0.00554821i	0.999996	−	0.00277410i	$-0.000883026\pi$
$882$		0			0
$883$	28.9462			0.974116			0.487058	−	0.873370i	$-0.338070\pi$
$883$	28.9462			0.974116			0.487058	+	0.873370i	$0.338070\pi$
$884$	−55.0002	+	48.4214i	−1.84986	+	1.62859i
$885$		0			0
$886$	−15.1595	+	33.5436i	−0.509294	+	1.12692i
$887$	20.3345	−	35.2204i	0.682766	−	1.18258i	−0.291368	−	0.956611i	$-0.594110\pi$
$887$	20.3345	−	35.2204i	0.682766	−	1.18258i	0.974133	−	0.225974i	$-0.0725564\pi$
$888$		0			0
$889$	47.6308	+	11.5582i	1.59749	+	0.387651i
$890$	−0.768485	+	0.551808i	−0.0257597	+	0.0184967i
$891$		0			0
$892$	17.1840	−	3.45251i	0.575364	−	0.115599i
$893$	−0.575078	+	0.332021i	−0.0192442	+	0.0111107i
$894$		0			0
$895$	−5.90642			−0.197430
$896$	−13.1787	−	26.8761i	−0.440269	−	0.897866i
$897$		0			0
$898$	−15.2764	+	1.51944i	−0.509781	+	0.0507044i
$899$	5.02810	−	2.90297i	0.167696	−	0.0968196i
$900$		0			0
$901$	8.92054	−	15.4508i	0.297186	−	0.514742i
$902$	18.7836	−	13.4875i	0.625425	−	0.449085i
$903$		0			0
$904$	−0.388253	+	0.119000i	−0.0129131	+	0.00395790i
$905$	−1.95343	+	3.38344i	−0.0649343	+	0.112469i
$906$		0			0
$907$	6.57673	+	11.3912i	0.218377	+	0.378240i	0.954312	−	0.298813i	$-0.0965905\pi$
$907$	6.57673	+	11.3912i	0.218377	+	0.378240i	−0.735935	+	0.677052i	$0.763257\pi$
$908$	8.83518	−	7.77837i	0.293206	−	0.258134i
$909$		0			0
$910$	3.47797	+	2.71335i	0.115293	+	0.0899468i
$911$			4.58131i			0.151785i	0.997116	+	0.0758927i	$0.0241806\pi$
$911$			4.58131i			0.151785i	−0.997116	+	0.0758927i	$0.975819\pi$
$912$		0			0
$913$	11.7780	−	6.80002i	0.389794	−	0.225048i
$914$	−17.5098	+	38.7442i	−0.579174	+	1.28154i
$915$		0			0
$916$	−10.1034	+	29.9530i	−0.333827	+	0.989675i
$917$	−23.9464	+	25.1111i	−0.790779	+	0.829242i
$918$		0			0
$919$	−22.6967	−	13.1039i	−0.748694	−	0.432259i	0.0765280	−	0.997067i	$-0.475617\pi$
$919$	−22.6967	−	13.1039i	−0.748694	−	0.432259i	−0.825222	+	0.564809i	$0.808950\pi$
$920$	−3.30067	+	3.54454i	−0.108820	+	0.116860i
$921$		0			0
$922$	12.9980	−	1.29282i	0.428065	−	0.0425767i
$923$		−	41.0957i		−	1.35268i
$924$		0			0
$925$		−	36.8360i		−	1.21116i
$926$	2.43015	+	24.4327i	0.0798597	+	0.802908i
$927$		0			0
$928$	−7.55535	−	13.9729i	−0.248017	−	0.458684i
$929$	−4.55350	−	2.62897i	−0.149396	−	0.0862536i	0.423439	−	0.905925i	$-0.360823\pi$
$929$	−4.55350	−	2.62897i	−0.149396	−	0.0862536i	−0.572834	+	0.819671i	$0.694156\pi$
$930$		0			0
$931$	−0.882506	−	1.37358i	−0.0289230	−	0.0450172i
$932$	0.203379	−	0.602946i	0.00666191	−	0.0197501i
$933$		0			0
$934$	−28.1190	−	12.7079i	−0.920081	−	0.415817i
$935$	−6.39929	+	3.69463i	−0.209279	+	0.120827i
$936$		0			0
$937$			4.17839i			0.136502i	0.997668	+	0.0682510i	$0.0217419\pi$
$937$			4.17839i			0.136502i	−0.997668	+	0.0682510i	$0.978258\pi$
$938$	−6.01985	+	2.43710i	−0.196555	+	0.0795740i
$939$		0			0
$940$	−0.968567	−	1.10016i	−0.0315912	−	0.0358833i
$941$	−9.55498	−	16.5497i	−0.311483	−	0.539505i	0.667200	−	0.744878i	$-0.267492\pi$
$941$	−9.55498	−	16.5497i	−0.311483	−	0.539505i	−0.978684	+	0.205373i	$0.934159\pi$
$942$		0			0
$943$	−15.1569	+	26.2526i	−0.493577	+	0.854901i
$944$	−6.00652	+	7.89056i	−0.195496	+	0.256816i
$945$		0			0
$946$	16.0638	+	22.3715i	0.522280	+	0.727362i
$947$	−1.20797	+	2.09227i	−0.0392539	+	0.0679897i	−0.884985	−	0.465620i	$-0.845831\pi$
$947$	−1.20797	+	2.09227i	−0.0392539	+	0.0679897i	0.845731	+	0.533610i	$0.179165\pi$
$948$		0			0
$949$	−30.1280	+	17.3944i	−0.977995	+	0.564646i
$950$	0.161068	+	1.61938i	0.00522574	+	0.0525395i
$951$		0			0
$952$	32.9555	+	49.9786i	1.06809	+	1.61982i
$953$	−9.71810			−0.314800			−0.157400	−	0.987535i	$-0.550311\pi$
$953$	−9.71810			−0.314800			−0.157400	+	0.987535i	$0.550311\pi$
$954$		0			0
$955$	4.78741	−	2.76401i	0.154917	−	0.0894414i
$956$	−0.578404	−	2.87886i	−0.0187069	−	0.0931091i
$957$		0			0
$958$	−16.8363	−	23.4473i	−0.543955	−	0.757547i
$959$	−6.41426	+	1.88297i	−0.207127	+	0.0608041i
$960$		0			0
$961$	13.3625	−	23.1446i	0.431049	−	0.746598i
$962$	−44.0668	−	19.9153i	−1.42077	−	0.642095i
$963$		0			0
$964$	−22.2478	+	19.5867i	−0.716553	+	0.630844i
$965$	−1.84328			−0.0593372
$966$		0			0
$967$			46.0680i			1.48145i	0.671809	+	0.740724i	$0.265517\pi$
$967$			46.0680i			1.48145i	−0.671809	+	0.740724i	$0.734483\pi$
$968$	−1.18966	+	5.16960i	−0.0382370	+	0.166157i
$969$		0			0
$970$	−4.84413	−	2.18923i	−0.155536	−	0.0702920i
$971$	−10.3074	−	5.95095i	−0.330779	−	0.190975i	0.325408	−	0.945574i	$-0.394498\pi$
$971$	−10.3074	−	5.95095i	−0.330779	−	0.190975i	−0.656187	+	0.754599i	$0.727832\pi$
$972$		0			0
$973$	−43.2001	−	10.4831i	−1.38493	−	0.336071i
$974$	9.71474	−	6.97564i	0.311280	−	0.223514i
$975$		0			0
$976$	−4.50325	+	35.2537i	−0.144145	+	1.12844i
$977$	16.1299	+	27.9379i	0.516042	+	0.893811i	0.999827	+	0.0186241i	$0.00592857\pi$
$977$	16.1299	+	27.9379i	0.516042	+	0.893811i	−0.483784	+	0.875187i	$0.660738\pi$
$978$		0			0
$979$		−	9.32524i		−	0.298036i
$980$	2.58884	−	2.50705i	0.0826976	−	0.0800849i
$981$		0			0
$982$	−52.7476	+	5.24644i	−1.68324	+	0.167421i
$983$	25.6985	+	44.5110i	0.819653	+	1.41968i	0.905938	+	0.423411i	$0.139167\pi$
$983$	25.6985	+	44.5110i	0.819653	+	1.41968i	−0.0862842	+	0.996271i	$0.527499\pi$
$984$		0			0
$985$	2.07232	+	1.19646i	0.0660297	+	0.0381223i
$986$	18.5297	+	25.8057i	0.590106	+	0.821821i
$987$		0			0
$988$	2.02434	+	0.682827i	0.0644027	+	0.0217236i
$989$	−31.2672	−	18.0521i	−0.994240	−	0.574025i
$990$		0			0
$991$	10.5357	−	6.08280i	0.334678	−	0.193226i	−0.323238	−	0.946318i	$-0.604771\pi$
$991$	10.5357	−	6.08280i	0.334678	−	0.193226i	0.657916	+	0.753091i	$0.271438\pi$
$992$	9.96197	+	6.12848i	0.316293	+	0.194580i
$993$		0			0
$994$	−33.2505	−	4.64925i	−1.05464	−	0.147465i
$995$	5.34881			0.169569
$996$		0			0
$997$	7.92001	+	13.7179i	0.250829	+	0.434449i	0.963754	−	0.266791i	$-0.0859634\pi$
$997$	7.92001	+	13.7179i	0.250829	+	0.434449i	−0.712925	+	0.701240i	$0.752630\pi$
$998$	−7.26085	+	16.0661i	−0.229838	+	0.508565i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.c.19.15		32
3.2	odd	2		168.2.t.a.19.2	✓	32
4.3	odd	2		2016.2.bs.c.271.8		32
7.3	odd	6	inner	504.2.bk.c.451.6		32
8.3	odd	2	inner	504.2.bk.c.19.6		32
8.5	even	2		2016.2.bs.c.271.9		32
12.11	even	2		672.2.bb.a.271.13		32
21.2	odd	6		1176.2.p.a.979.23		32
21.5	even	6		1176.2.p.a.979.24		32
21.17	even	6		168.2.t.a.115.11	yes	32
24.5	odd	2		672.2.bb.a.271.12		32
24.11	even	2		168.2.t.a.19.11	yes	32
28.3	even	6		2016.2.bs.c.1711.9		32
56.3	even	6	inner	504.2.bk.c.451.15		32
56.45	odd	6		2016.2.bs.c.1711.8		32
84.23	even	6		4704.2.p.a.3919.32		32
84.47	odd	6		4704.2.p.a.3919.27		32
84.59	odd	6		672.2.bb.a.367.12		32
168.5	even	6		4704.2.p.a.3919.31		32
168.59	odd	6		168.2.t.a.115.2	yes	32
168.101	even	6		672.2.bb.a.367.13		32
168.107	even	6		1176.2.p.a.979.22		32
168.131	odd	6		1176.2.p.a.979.21		32
168.149	odd	6		4704.2.p.a.3919.28		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.2	✓	32	3.2	odd	2
168.2.t.a.19.11	yes	32	24.11	even	2
168.2.t.a.115.2	yes	32	168.59	odd	6
168.2.t.a.115.11	yes	32	21.17	even	6
504.2.bk.c.19.6		32	8.3	odd	2	inner
504.2.bk.c.19.15		32	1.1	even	1	trivial
504.2.bk.c.451.6		32	7.3	odd	6	inner
504.2.bk.c.451.15		32	56.3	even	6	inner
672.2.bb.a.271.12		32	24.5	odd	2
672.2.bb.a.271.13		32	12.11	even	2
672.2.bb.a.367.12		32	84.59	odd	6
672.2.bb.a.367.13		32	168.101	even	6
1176.2.p.a.979.21		32	168.131	odd	6
1176.2.p.a.979.22		32	168.107	even	6
1176.2.p.a.979.23		32	21.2	odd	6
1176.2.p.a.979.24		32	21.5	even	6
2016.2.bs.c.271.8		32	4.3	odd	2
2016.2.bs.c.271.9		32	8.5	even	2
2016.2.bs.c.1711.8		32	56.45	odd	6
2016.2.bs.c.1711.9		32	28.3	even	6
4704.2.p.a.3919.27		32	84.47	odd	6
4704.2.p.a.3919.28		32	168.149	odd	6
4704.2.p.a.3919.31		32	168.5	even	6
4704.2.p.a.3919.32		32	84.23	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)

\(f(q)\)	\(=\)	\(q+(1.40727 - 0.139971i) q^{2} +(1.96082 - 0.393955i) q^{4} +(-0.128707 + 0.222928i) q^{5} +(0.623918 - 2.57113i) q^{7} +(2.70425 - 0.828860i) q^{8} +O(q^{10})\)	\(q+(1.40727 - 0.139971i) q^{2} +(1.96082 - 0.393955i) q^{4} +(-0.128707 + 0.222928i) q^{5} +(0.623918 - 2.57113i) q^{7} +(2.70425 - 0.828860i) q^{8} +(-0.149923 + 0.331735i) q^{10} +(-1.79412 - 3.10751i) q^{11} +4.57992 q^{13} +(0.518136 - 3.70561i) q^{14} +(3.68960 - 1.54495i) q^{16} +(-6.92813 + 3.99996i) q^{17} +(0.201988 + 0.116618i) q^{19} +(-0.164548 + 0.487825i) q^{20} +(-2.95978 - 4.12198i) q^{22} +(5.76102 + 3.32613i) q^{23} +(2.46687 + 4.27274i) q^{25} +(6.44518 - 0.641058i) q^{26} +(0.210478 - 5.28731i) q^{28} -2.80806i q^{29} +(1.03380 + 1.79060i) q^{31} +(4.97601 - 2.69060i) q^{32} +(-9.18987 + 6.59876i) q^{34} +(0.492874 + 0.470013i) q^{35} +(-6.46587 - 3.73307i) q^{37} +(0.300574 + 0.135840i) q^{38} +(-0.163282 + 0.709534i) q^{40} +4.55693i q^{41} -5.42738 q^{43} +(-4.74216 - 5.38645i) q^{44} +(8.57287 + 3.87438i) q^{46} +(-1.42355 + 2.46565i) q^{47} +(-6.22145 - 3.20835i) q^{49} +(4.06961 + 5.66761i) q^{50} +(8.98037 - 1.80428i) q^{52} +(-1.93137 + 1.11508i) q^{53} +0.923668 q^{55} +(-0.443874 - 7.47014i) q^{56} +(-0.393048 - 3.95170i) q^{58} +(-2.14701 + 1.23958i) q^{59} +(-4.44251 + 7.69466i) q^{61} +(1.70547 + 2.37515i) q^{62} +(6.62598 - 4.48289i) q^{64} +(-0.589469 + 1.02099i) q^{65} +(-0.867859 - 1.50318i) q^{67} +(-12.0090 + 10.5726i) q^{68} +(0.759395 + 0.592446i) q^{70} -8.97302i q^{71} +(-6.57828 + 3.79797i) q^{73} +(-9.62174 - 4.34840i) q^{74} +(0.442003 + 0.149092i) q^{76} +(-9.10921 + 2.67409i) q^{77} +(7.51791 + 4.34047i) q^{79} +(-0.130467 + 1.02136i) q^{80} +(0.637840 + 6.41283i) q^{82} +3.79017i q^{83} -2.05930i q^{85} +(-7.63778 + 0.759678i) q^{86} +(-7.42745 - 6.91643i) q^{88} +(2.25065 + 1.29941i) q^{89} +(2.85749 - 11.7756i) q^{91} +(12.6066 + 4.25234i) q^{92} +(-1.65819 + 3.66910i) q^{94} +(-0.0519946 + 0.0300191i) q^{95} +14.6024i q^{97} +(-9.20434 - 3.64419i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8}+O(q^{10}) \) 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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