LMFDB - Embedded newform 504.2.cj.e.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (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			37.1
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36256 - 0.378724i) q^{2} +(1.71314 + 1.03207i) q^{4} +(0.586448 + 0.338586i) q^{5} +(2.23683 + 1.41301i) q^{7} +(-1.94338 - 2.05506i) q^{8} +O(q^{10})$	\(q+(-1.36256 - 0.378724i) q^{2} +(1.71314 + 1.03207i) q^{4} +(0.586448 + 0.338586i) q^{5} +(2.23683 + 1.41301i) q^{7} +(-1.94338 - 2.05506i) q^{8} +(-0.670840 - 0.683446i) q^{10} +(1.44721 - 0.835550i) q^{11} -1.28049i q^{13} +(-2.51267 - 2.77245i) q^{14} +(1.86967 + 3.53615i) q^{16} +(3.18262 + 5.51246i) q^{17} +(-2.20912 - 1.27544i) q^{19} +(0.655221 + 1.18530i) q^{20} +(-2.28836 + 0.590391i) q^{22} +(-0.127760 + 0.221287i) q^{23} +(-2.27072 - 3.93300i) q^{25} +(-0.484953 + 1.74474i) q^{26} +(2.37367 + 4.72924i) q^{28} +6.27489i q^{29} +(2.14368 + 3.71296i) q^{31} +(-1.20831 - 5.52630i) q^{32} +(-2.24881 - 8.71639i) q^{34} +(0.833358 + 1.58602i) q^{35} +(5.62313 + 3.24651i) q^{37} +(2.52702 + 2.57451i) q^{38} +(-0.443876 - 1.86319i) q^{40} +6.43132 q^{41} -5.48802i q^{43} +(3.34162 + 0.0622148i) q^{44} +(0.257887 - 0.253131i) q^{46} +(4.73403 - 8.19958i) q^{47} +(3.00680 + 6.32132i) q^{49} +(1.60447 + 6.21892i) q^{50} +(1.32155 - 2.19365i) q^{52} +(4.91784 - 2.83932i) q^{53} +1.13162 q^{55} +(-1.44318 - 7.34283i) q^{56} +(2.37645 - 8.54991i) q^{58} +(-8.74078 + 5.04649i) q^{59} +(13.2038 + 7.62324i) q^{61} +(-1.51470 - 5.87099i) q^{62} +(-0.446552 + 7.98753i) q^{64} +(0.433556 - 0.750941i) q^{65} +(-13.6595 + 7.88629i) q^{67} +(-0.236977 + 12.7283i) q^{68} +(-0.534837 - 2.47665i) q^{70} +5.48693 q^{71} +(-1.43261 - 2.48136i) q^{73} +(-6.43231 - 6.55318i) q^{74} +(-2.46819 - 4.46496i) q^{76} +(4.41781 + 0.175948i) q^{77} +(6.09527 - 10.5573i) q^{79} +(-0.100827 + 2.70681i) q^{80} +(-8.76305 - 2.43570i) q^{82} -7.63129i q^{83} +4.31036i q^{85} +(-2.07845 + 7.47776i) q^{86} +(-4.52959 - 1.35032i) q^{88} +(3.40374 - 5.89546i) q^{89} +(1.80935 - 2.86424i) q^{91} +(-0.447253 + 0.247237i) q^{92} +(-9.55577 + 9.37952i) q^{94} +(-0.863690 - 1.49595i) q^{95} -0.477890 q^{97} +(-1.70291 - 9.75193i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.36256	−	0.378724i	−0.963475	−	0.267799i
$2$	−1.36256	−	0.378724i	−0.963475	−	0.267799i
$3$		0			0
$3$		0			0
$4$	1.71314	+	1.03207i	0.856568	+	0.516034i
$5$	0.586448	+	0.338586i	0.262268	+	0.151420i	0.625369	−	0.780330i	$-0.284949\pi$
$5$	0.586448	+	0.338586i	0.262268	+	0.151420i	−0.363101	+	0.931750i	$0.618282\pi$
$6$		0			0
$7$	2.23683	+	1.41301i	0.845442	+	0.534068i
$7$	2.23683	+	1.41301i	0.845442	+	0.534068i
$8$	−1.94338	−	2.05506i	−0.687088	−	0.726574i
$9$		0			0
$10$	−0.670840	−	0.683446i	−0.212138	−	0.216124i
$11$	1.44721	−	0.835550i	0.436352	−	0.251928i	−0.265697	−	0.964057i	$-0.585602\pi$
$11$	1.44721	−	0.835550i	0.436352	−	0.251928i	0.702049	+	0.712129i	$0.252269\pi$
$12$		0			0
$13$		−	1.28049i		−	0.355144i	−0.984108	−	0.177572i	$-0.943176\pi$
$13$		−	1.28049i		−	0.355144i	0.984108	−	0.177572i	$-0.0568243\pi$
$14$	−2.51267	−	2.77245i	−0.671539	−	0.740969i
$15$		0			0
$16$	1.86967	+	3.53615i	0.467417	+	0.884037i
$17$	3.18262	+	5.51246i	0.771899	+	1.33697i	0.936521	+	0.350611i	$0.114026\pi$
$17$	3.18262	+	5.51246i	0.771899	+	1.33697i	−0.164622	+	0.986357i	$0.552640\pi$
$18$		0			0
$19$	−2.20912	−	1.27544i	−0.506807	−	0.292605i	0.224713	−	0.974425i	$-0.427856\pi$
$19$	−2.20912	−	1.27544i	−0.506807	−	0.292605i	−0.731520	+	0.681820i	$0.761189\pi$
$20$	0.655221	+	1.18530i	0.146512	+	0.265041i
$21$		0			0
$22$	−2.28836	+	0.590391i	−0.487880	+	0.125872i
$23$	−0.127760	+	0.221287i	−0.0266398	+	0.0461415i	−0.879038	−	0.476752i	$-0.841814\pi$
$23$	−0.127760	+	0.221287i	−0.0266398	+	0.0461415i	0.852398	+	0.522893i	$0.175147\pi$
$24$		0			0
$25$	−2.27072	−	3.93300i	−0.454144	−	0.786600i
$26$	−0.484953	+	1.74474i	−0.0951071	+	0.342172i
$27$		0			0
$28$	2.37367	+	4.72924i	0.448581	+	0.893742i
$29$			6.27489i			1.16522i	0.812753	+	0.582609i	$0.197968\pi$
$29$			6.27489i			1.16522i	−0.812753	+	0.582609i	$0.802032\pi$
$30$		0			0
$31$	2.14368	+	3.71296i	0.385016	+	0.666867i	0.991771	−	0.128022i	$-0.0408627\pi$
$31$	2.14368	+	3.71296i	0.385016	+	0.666867i	−0.606756	+	0.794888i	$0.707529\pi$
$32$	−1.20831	−	5.52630i	−0.213601	−	0.976921i
$33$		0			0
$34$	−2.24881	−	8.71639i	−0.385667	−	1.49485i
$35$	0.833358	+	1.58602i	0.140863	+	0.268086i
$36$		0			0
$37$	5.62313	+	3.24651i	0.924436	+	0.533724i	0.885048	−	0.465500i	$-0.154126\pi$
$37$	5.62313	+	3.24651i	0.924436	+	0.533724i	0.0393887	+	0.999224i	$0.487459\pi$
$38$	2.52702	+	2.57451i	0.409937	+	0.417640i
$39$		0			0
$40$	−0.443876	−	1.86319i	−0.0701830	−	0.294596i
$41$	6.43132			1.00440			0.502202	−	0.864751i	$-0.332524\pi$
$41$	6.43132			1.00440			0.502202	+	0.864751i	$0.332524\pi$
$42$		0			0
$43$		−	5.48802i		−	0.836916i	−0.908236	−	0.418458i	$-0.862571\pi$
$43$		−	5.48802i		−	0.836916i	0.908236	−	0.418458i	$-0.137429\pi$
$44$	3.34162	+	0.0622148i	0.503768	+	0.00937924i
$45$		0			0
$46$	0.257887	−	0.253131i	0.0380234	−	0.0373221i
$47$	4.73403	−	8.19958i	0.690529	−	1.19603i	−0.281136	−	0.959668i	$-0.590711\pi$
$47$	4.73403	−	8.19958i	0.690529	−	1.19603i	0.971665	−	0.236363i	$-0.0759556\pi$
$48$		0			0
$49$	3.00680	+	6.32132i	0.429543	+	0.903046i
$50$	1.60447	+	6.21892i	0.226906	+	0.879489i
$51$		0			0
$52$	1.32155	−	2.19365i	0.183267	−	0.304205i
$53$	4.91784	−	2.83932i	0.675518	−	0.390010i	−0.122647	−	0.992450i	$-0.539138\pi$
$53$	4.91784	−	2.83932i	0.675518	−	0.390010i	0.798164	+	0.602440i	$0.205805\pi$
$54$		0			0
$55$	1.13162			0.152588
$56$	−1.44318	−	7.34283i	−0.192854	−	0.981228i
$57$		0			0
$58$	2.37645	−	8.54991i	0.312044	−	1.12266i
$59$	−8.74078	+	5.04649i	−1.13795	+	0.656997i	−0.945923	−	0.324392i	$-0.894840\pi$
$59$	−8.74078	+	5.04649i	−1.13795	+	0.656997i	−0.192030	+	0.981389i	$0.561507\pi$
$60$		0			0
$61$	13.2038	+	7.62324i	1.69058	+	0.976056i	0.954049	+	0.299650i	$0.0968698\pi$
$61$	13.2038	+	7.62324i	1.69058	+	0.976056i	0.736529	+	0.676406i	$0.236464\pi$
$62$	−1.51470	−	5.87099i	−0.192367	−	0.745616i
$63$		0			0
$64$	−0.446552	+	7.98753i	−0.0558190	+	0.998441i
$65$	0.433556	−	0.750941i	0.0537760	−	0.0931428i
$66$		0			0
$67$	−13.6595	+	7.88629i	−1.66877	+	0.963464i	−0.700465	+	0.713687i	$0.747024\pi$
$67$	−13.6595	+	7.88629i	−1.66877	+	0.963464i	−0.968304	+	0.249776i	$0.919643\pi$
$68$	−0.236977	+	12.7283i	−0.0287377	+	1.54353i
$69$		0			0
$70$	−0.534837	−	2.47665i	−0.0639253	−	0.296017i
$71$	5.48693			0.651179			0.325589	−	0.945511i	$-0.394437\pi$
$71$	5.48693			0.651179			0.325589	+	0.945511i	$0.394437\pi$
$72$		0			0
$73$	−1.43261	−	2.48136i	−0.167675	−	0.290421i	0.769927	−	0.638132i	$-0.220293\pi$
$73$	−1.43261	−	2.48136i	−0.167675	−	0.290421i	−0.937602	+	0.347711i	$0.886959\pi$
$74$	−6.43231	−	6.55318i	−0.747741	−	0.761792i
$75$		0			0
$76$	−2.46819	−	4.46496i	−0.283120	−	0.512166i
$77$	4.41781	+	0.175948i	0.503456	+	0.0200511i
$78$		0			0
$79$	6.09527	−	10.5573i	0.685771	−	1.18779i	−0.287423	−	0.957804i	$-0.592798\pi$
$79$	6.09527	−	10.5573i	0.685771	−	1.18779i	0.973194	−	0.229986i	$-0.0738682\pi$
$80$	−0.100827	+	2.70681i	−0.0112728	+	0.302631i
$81$		0			0
$82$	−8.76305	−	2.43570i	−0.967717	−	0.268978i
$83$		−	7.63129i		−	0.837643i	−0.908069	−	0.418822i	$-0.862443\pi$
$83$		−	7.63129i		−	0.837643i	0.908069	−	0.418822i	$-0.137557\pi$
$84$		0			0
$85$			4.31036i			0.467525i
$86$	−2.07845	+	7.47776i	−0.224125	+	0.806347i
$87$		0			0
$88$	−4.52959	−	1.35032i	−0.482856	−	0.143945i
$89$	3.40374	−	5.89546i	0.360796	−	0.624917i	−0.627296	−	0.778781i	$-0.715838\pi$
$89$	3.40374	−	5.89546i	0.360796	−	0.624917i	0.988092	+	0.153864i	$0.0491717\pi$
$90$		0			0
$91$	1.80935	−	2.86424i	0.189671	−	0.300254i
$92$	−0.447253	+	0.247237i	−0.0466294	+	0.0257763i
$93$		0			0
$94$	−9.55577	+	9.37952i	−0.985603	+	0.967424i
$95$	−0.863690	−	1.49595i	−0.0886127	−	0.153482i
$96$		0			0
$97$	−0.477890			−0.0485224			−0.0242612	−	0.999706i	$-0.507723\pi$
$97$	−0.477890			−0.0485224			−0.0242612	+	0.999706i	$0.507723\pi$
$98$	−1.70291	−	9.75193i	−0.172020	−	0.985093i
$99$		0			0
$100$	0.169077	−	9.08130i	0.0169077	−	0.908130i
$101$	−11.4161	+	6.59108i	−1.13594	+	0.655837i	−0.945423	−	0.325846i	$-0.894351\pi$
$101$	−11.4161	+	6.59108i	−1.13594	+	0.655837i	−0.190520	+	0.981683i	$0.561018\pi$
$102$		0			0
$103$	−0.808712	+	1.40073i	−0.0796848	+	0.138018i	−0.903114	−	0.429401i	$-0.858725\pi$
$103$	−0.808712	+	1.40073i	−0.0796848	+	0.138018i	0.823429	+	0.567419i	$0.192058\pi$
$104$	−2.63149	+	2.48848i	−0.258038	+	0.244015i
$105$		0			0
$106$	−7.77617	+	2.00623i	−0.755288	+	0.194862i
$107$	−9.65085	−	5.57192i	−0.932983	−	0.538658i	−0.0452293	−	0.998977i	$-0.514402\pi$
$107$	−9.65085	−	5.57192i	−0.932983	−	0.538658i	−0.887754	+	0.460319i	$0.847735\pi$
$108$		0			0
$109$	−3.49609	+	2.01847i	−0.334865	+	0.193334i	−0.657999	−	0.753019i	$-0.728597\pi$
$109$	−3.49609	+	2.01847i	−0.334865	+	0.193334i	0.323134	+	0.946353i	$0.395264\pi$
$110$	−1.54190	−	0.428573i	−0.147015	−	0.0408628i
$111$		0			0
$112$	−0.814486	+	10.5516i	−0.0769617	+	0.997034i
$113$	−20.3522			−1.91458			−0.957288	−	0.289137i	$-0.906632\pi$
$113$	−20.3522			−1.91458			−0.957288	+	0.289137i	$0.906632\pi$
$114$		0			0
$115$	−0.149849	+	0.0865155i	−0.0139735	+	0.00806761i
$116$	−6.47612	+	10.7497i	−0.601293	+	0.998088i
$117$		0			0
$118$	13.8211	−	3.56580i	1.27233	−	0.328258i
$119$	−0.670187	+	16.8275i	−0.0614359	+	1.54257i
$120$		0			0
$121$	−4.10371	+	7.10784i	−0.373065	+	0.646167i
$122$	−15.1039	−	15.3877i	−1.36744	−	1.39314i
$123$		0			0
$124$	−0.159618	+	8.57322i	−0.0143341	+	0.769898i
$125$		−	6.46119i		−	0.577907i
$126$		0			0
$127$	−15.3981			−1.36636			−0.683181	−	0.730249i	$-0.739404\pi$
$127$	−15.3981			−1.36636			−0.683181	+	0.730249i	$0.739404\pi$
$128$	3.63352	−	10.7144i	0.321161	−	0.947025i
$129$		0			0
$130$	−0.875146	+	0.859004i	−0.0767553	+	0.0753396i
$131$	1.96999	+	1.13738i	0.172119	+	0.0993730i	0.583585	−	0.812052i	$-0.301650\pi$
$131$	1.96999	+	1.13738i	0.172119	+	0.0993730i	−0.411466	+	0.911425i	$0.634983\pi$
$132$		0			0
$133$	−3.13922	−	5.97444i	−0.272205	−	0.518050i
$134$	21.5985	−	5.57237i	1.86583	−	0.481379i
$135$		0			0
$136$	5.14340	−	17.2533i	0.441043	−	1.47946i
$137$	−3.42016	−	5.92390i	−0.292204	−	0.506113i	0.682126	−	0.731234i	$-0.261055\pi$
$137$	−3.42016	−	5.92390i	−0.292204	−	0.506113i	−0.974331	+	0.225122i	$0.927722\pi$
$138$		0			0
$139$		−	7.65594i		−	0.649369i	−0.945822	−	0.324684i	$-0.894742\pi$
$139$		−	7.65594i		−	0.649369i	0.945822	−	0.324684i	$-0.105258\pi$
$140$	−0.209221	+	3.57714i	−0.0176824	+	0.302324i
$141$		0			0
$142$	−7.47626	−	2.07803i	−0.627394	−	0.174385i
$143$	−1.06991	−	1.85314i	−0.0894706	−	0.154968i
$144$		0			0
$145$	−2.12459	+	3.67990i	−0.176438	+	0.305599i
$146$	1.01227	+	3.92357i	0.0837761	+	0.324717i
$147$		0			0
$148$	6.28255	+	11.3652i	0.516423	+	0.934211i
$149$	11.6538	+	6.72830i	0.954714	+	0.551204i	0.894542	−	0.446984i	$-0.147502\pi$
$149$	11.6538	+	6.72830i	0.954714	+	0.551204i	0.0601715	+	0.998188i	$0.480835\pi$
$150$		0			0
$151$	−7.92722	−	13.7303i	−0.645108	−	1.11736i	−0.984277	−	0.176634i	$-0.943479\pi$
$151$	−7.92722	−	13.7303i	−0.645108	−	1.11736i	0.339169	−	0.940726i	$-0.389854\pi$
$152$	1.67206	+	7.01854i	0.135622	+	0.569278i
$153$		0			0
$154$	−5.95289	−	1.91287i	−0.479698	−	0.154144i
$155$			2.90328i			0.233197i
$156$		0			0
$157$	−10.5037	+	6.06431i	−0.838286	+	0.483985i	−0.856681	−	0.515846i	$-0.827478\pi$
$157$	−10.5037	+	6.06431i	−0.838286	+	0.483985i	0.0183949	+	0.999831i	$0.494144\pi$
$158$	−12.3035	+	12.0765i	−0.978812	+	0.960758i
$159$		0			0
$160$	1.16252	−	3.65000i	0.0919051	−	0.288558i
$161$	−0.598458	+	0.314454i	−0.0471651	+	0.0247825i
$162$		0			0
$163$	−17.6931	−	10.2151i	−1.38583	−	0.800112i	−0.392992	−	0.919542i	$-0.628560\pi$
$163$	−17.6931	−	10.2151i	−1.38583	−	0.800112i	−0.992843	+	0.119430i	$0.961893\pi$
$164$	11.0177	+	6.63756i	0.860340	+	0.518307i
$165$		0			0
$166$	−2.89016	+	10.3981i	−0.224320	+	0.807048i
$167$	−5.90808			−0.457181			−0.228591	−	0.973523i	$-0.573412\pi$
$167$	−5.90808			−0.457181			−0.228591	+	0.973523i	$0.573412\pi$
$168$		0			0
$169$	11.3603			0.873873
$170$	1.63244	−	5.87313i	0.125202	−	0.450448i
$171$		0			0
$172$	5.66402	−	9.40173i	0.431877	−	0.716875i
$173$	3.75589	+	2.16847i	0.285555	+	0.164865i	0.635936	−	0.771742i	$-0.280614\pi$
$173$	3.75589	+	2.16847i	0.285555	+	0.164865i	−0.350380	+	0.936608i	$0.613948\pi$
$174$		0			0
$175$	0.478161	−	12.0060i	0.0361456	−	0.907568i
$176$	5.66044	+	3.55536i	0.426672	+	0.267996i
$177$		0			0
$178$	−6.87056	+	6.74383i	−0.514970	+	0.505471i
$179$	5.46686	−	3.15629i	0.408612	−	0.235912i	−0.281581	−	0.959537i	$-0.590859\pi$
$179$	5.46686	−	3.15629i	0.408612	−	0.235912i	0.690193	+	0.723625i	$0.257525\pi$
$180$		0			0
$181$		−	12.0671i		−	0.896938i	−0.893798	−	0.448469i	$-0.851969\pi$
$181$		−	12.0671i		−	0.896938i	0.893798	−	0.448469i	$-0.148031\pi$
$182$	−3.55010	+	3.21745i	−0.263151	+	0.238493i
$183$		0			0
$184$	0.703044	−	0.167490i	0.0518291	−	0.0123475i
$185$	2.19845	+	3.80782i	0.161633	+	0.279957i
$186$		0			0
$187$	9.21187	+	5.31848i	0.673639	+	0.388925i
$188$	16.5726	−	9.16115i	1.20868	−	0.668145i
$189$		0			0
$190$	0.610274	+	2.36543i	0.0442739	+	0.171606i
$191$	−3.97889	+	6.89164i	−0.287902	+	0.498662i	−0.973309	−	0.229499i	$-0.926291\pi$
$191$	−3.97889	+	6.89164i	−0.287902	+	0.498662i	0.685406	+	0.728161i	$0.259625\pi$
$192$		0			0
$193$	−3.07064	−	5.31851i	−0.221030	−	0.382835i	0.734091	−	0.679051i	$-0.237608\pi$
$193$	−3.07064	−	5.31851i	−0.221030	−	0.382835i	−0.955121	+	0.296216i	$0.904275\pi$
$194$	0.651153	+	0.180988i	0.0467501	+	0.0129942i
$195$		0			0
$196$	−1.37298	+	13.9325i	−0.0980698	+	0.995180i
$197$		−	15.1633i		−	1.08034i	−0.841556	−	0.540170i	$-0.818360\pi$
$197$		−	15.1633i		−	1.08034i	0.841556	−	0.540170i	$-0.181640\pi$
$198$		0			0
$199$	7.02616	+	12.1697i	0.498071	+	0.862685i	0.999998	−	0.00222556i	$-0.000708420\pi$
$199$	7.02616	+	12.1697i	0.498071	+	0.862685i	−0.501926	+	0.864910i	$0.667375\pi$
$200$	−3.66969	+	12.3098i	−0.259486	+	0.870433i
$201$		0			0
$202$	18.0513	−	4.65719i	1.27009	−	0.327679i
$203$	−8.86648	+	14.0359i	−0.622305	+	0.985124i
$204$		0			0
$205$	3.77164	+	2.17755i	0.263422	+	0.152087i
$206$	1.63241	−	1.60230i	0.113735	−	0.111637i
$207$		0			0
$208$	4.52800	−	2.39409i	0.313961	−	0.166000i
$209$	−4.26276			−0.294861
$210$		0			0
$211$		−	10.2832i		−	0.707926i	−0.935259	−	0.353963i	$-0.884834\pi$
$211$		−	10.2832i		−	0.707926i	0.935259	−	0.353963i	$-0.115166\pi$
$212$	11.3553	+	0.211415i	0.779885	+	0.0145200i
$213$		0			0
$214$	11.0396	+	11.2471i	0.754654	+	0.768835i
$215$	1.85817	−	3.21844i	0.126726	−	0.219496i
$216$		0			0
$217$	−0.451409	+	11.3343i	−0.0306436	+	0.769421i
$218$	5.52807	−	1.42623i	0.374408	−	0.0965964i
$219$		0			0
$220$	1.93862	+	1.16791i	0.130702	+	0.0787406i
$221$	7.05865	−	4.07531i	0.474816	−	0.274135i
$222$		0			0
$223$	9.55799			0.640050			0.320025	−	0.947409i	$-0.396309\pi$
$223$	9.55799			0.640050			0.320025	+	0.947409i	$0.396309\pi$
$224$	5.10594	−	14.0687i	0.341155	−	0.940007i
$225$		0			0
$226$	27.7311	+	7.70788i	1.84465	+	0.512721i
$227$	23.7134	−	13.6909i	1.57391	−	0.908700i	0.578232	−	0.815872i	$-0.303743\pi$
$227$	23.7134	−	13.6909i	1.57391	−	0.908700i	0.995682	−	0.0928278i	$-0.0295906\pi$
$228$		0			0
$229$	10.2388	+	5.91138i	0.676599	+	0.390635i	0.798573	−	0.601899i	$-0.205589\pi$
$229$	10.2388	+	5.91138i	0.676599	+	0.390635i	−0.121973	+	0.992533i	$0.538922\pi$
$230$	0.236944	−	0.0611309i	0.0156236	−	0.00403085i
$231$		0			0
$232$	12.8953	−	12.1945i	0.846617	−	0.800608i
$233$	4.82097	−	8.35017i	0.315833	−	0.547038i	−0.663782	−	0.747926i	$-0.731050\pi$
$233$	4.82097	−	8.35017i	0.315833	−	0.547038i	0.979614	+	0.200889i	$0.0643829\pi$
$234$		0			0
$235$	5.55252	−	3.20575i	0.362207	−	0.209120i
$236$	−20.1825	−	0.375761i	−1.31377	−	0.0244599i
$237$		0			0
$238$	7.28616	−	22.6747i	0.472291	−	1.46978i
$239$	−14.9633			−0.967893			−0.483947	−	0.875098i	$-0.660797\pi$
$239$	−14.9633			−0.967893			−0.483947	+	0.875098i	$0.660797\pi$
$240$		0			0
$241$	−5.68537	−	9.84735i	−0.366227	−	0.634324i	0.622745	−	0.782425i	$-0.286017\pi$
$241$	−5.68537	−	9.84735i	−0.366227	−	0.634324i	−0.988972	+	0.148101i	$0.952684\pi$
$242$	8.28347	−	8.13068i	0.532481	−	0.522660i
$243$		0			0
$244$	14.7523	+	26.6869i	0.944417	+	1.70845i
$245$	−0.376977	+	4.72519i	−0.0240842	+	0.301881i
$246$		0			0
$247$	−1.63318	+	2.82876i	−0.103917	+	0.179990i
$248$	3.46438	−	11.6211i	0.219988	−	0.737939i
$249$		0			0
$250$	−2.44701	+	8.80376i	−0.154763	+	0.556799i
$251$		−	3.75699i		−	0.237139i	−0.992946	−	0.118570i	$-0.962169\pi$
$251$		−	3.75699i		−	0.237139i	0.992946	−	0.118570i	$-0.0378309\pi$
$252$		0			0
$253$			0.426999i			0.0268452i
$254$	20.9808	+	5.83164i	1.31646	+	0.365910i
$255$		0			0
$256$	−9.00868	+	13.2228i	−0.563043	+	0.826428i
$257$	−4.99709	+	8.65522i	−0.311710	+	0.539898i	−0.978733	−	0.205140i	$-0.934235\pi$
$257$	−4.99709	+	8.65522i	−0.311710	+	0.539898i	0.667023	+	0.745037i	$0.267568\pi$
$258$		0			0
$259$	7.99061	+	15.2074i	0.496513	+	0.944944i
$260$	1.51776	−	0.839004i	0.0941277	−	0.0520328i
$261$		0			0
$262$	−2.25348	−	2.29583i	−0.139221	−	0.141837i
$263$	−7.55841	−	13.0915i	−0.466071	−	0.807259i	0.533178	−	0.846003i	$-0.320998\pi$
$263$	−7.55841	−	13.0915i	−0.466071	−	0.807259i	−0.999249	+	0.0387438i	$0.987664\pi$
$264$		0			0
$265$	3.84541			0.236222
$266$	2.01471	+	9.32943i	0.123530	+	0.572024i
$267$		0			0
$268$	−31.5397	−	0.587211i	−1.92659	−	0.0358696i
$269$	−8.17624	+	4.72055i	−0.498514	+	0.287817i	−0.728100	−	0.685471i	$-0.759596\pi$
$269$	−8.17624	+	4.72055i	−0.498514	+	0.287817i	0.229586	+	0.973288i	$0.426263\pi$
$270$		0			0
$271$	−8.43032	+	14.6017i	−0.512106	+	0.886993i	0.487796	+	0.872958i	$0.337801\pi$
$271$	−8.43032	+	14.6017i	−0.512106	+	0.886993i	−0.999902	+	0.0140351i	$0.995532\pi$
$272$	−13.5424	+	21.5607i	−0.821131	+	1.30731i
$273$		0			0
$274$	2.41665	+	9.36696i	0.145995	+	0.565879i
$275$	−6.57244	−	3.79460i	−0.396333	−	0.228823i
$276$		0			0
$277$	7.77929	−	4.49138i	0.467412	−	0.269861i	−0.247744	−	0.968826i	$-0.579689\pi$
$277$	7.77929	−	4.49138i	0.467412	−	0.269861i	0.715156	+	0.698965i	$0.246356\pi$
$278$	−2.89949	+	10.4317i	−0.173900	+	0.625650i
$279$		0			0
$280$	1.63983	−	4.79483i	0.0979985	−	0.286546i
$281$	−22.6784			−1.35288			−0.676439	−	0.736498i	$-0.736478\pi$
$281$	−22.6784			−1.35288			−0.676439	+	0.736498i	$0.736478\pi$
$282$		0			0
$283$	16.0874	−	9.28805i	0.956296	−	0.552118i	0.0612647	−	0.998122i	$-0.480487\pi$
$283$	16.0874	−	9.28805i	0.956296	−	0.552118i	0.895031	+	0.446004i	$0.147153\pi$
$284$	9.39985	+	5.66289i	0.557779	+	0.336031i
$285$		0			0
$286$	0.755989	+	2.93022i	0.0447026	+	0.173268i
$287$	14.3858	+	9.08752i	0.849164	+	0.536419i
$288$		0			0
$289$	−11.7582	+	20.3657i	−0.691656	+	1.19798i
$290$	4.28855	−	4.20945i	0.251832	−	0.247187i
$291$		0			0
$292$	0.106672	−	5.72946i	0.00624251	−	0.335292i
$293$		−	15.5621i		−	0.909145i	−0.890710	−	0.454573i	$-0.849792\pi$
$293$		−	15.5621i		−	0.909145i	0.890710	−	0.454573i	$-0.150208\pi$
$294$		0			0
$295$	−6.83469			−0.397931
$296$	−4.25609	−	17.8651i	−0.247380	−	1.03839i
$297$		0			0
$298$	−13.3308	−	13.5813i	−0.772231	−	0.786742i
$299$	0.283356	+	0.163595i	0.0163869	+	0.00946097i
$300$		0			0
$301$	7.75463	−	12.2758i	0.446970	−	0.707563i
$302$	5.60129	+	21.7106i	0.322318	+	1.24931i
$303$		0			0
$304$	0.379809	−	10.1964i	0.0217835	−	0.584805i
$305$	5.16224	+	8.94127i	0.295589	+	0.511976i
$306$		0			0
$307$			28.8304i			1.64544i	0.568450	+	0.822718i	$0.307543\pi$
$307$			28.8304i			1.64544i	−0.568450	+	0.822718i	$0.692457\pi$
$308$	7.38672	+	4.86091i	0.420897	+	0.276976i
$309$		0			0
$310$	1.09954	−	3.95589i	0.0624497	−	0.224679i
$311$	−6.03436	−	10.4518i	−0.342177	−	0.592668i	0.642660	−	0.766152i	$-0.277831\pi$
$311$	−6.03436	−	10.4518i	−0.342177	−	0.592668i	−0.984837	+	0.173484i	$0.944498\pi$
$312$		0			0
$313$	14.5841	−	25.2604i	0.824343	−	1.42780i	−0.0780780	−	0.996947i	$-0.524878\pi$
$313$	14.5841	−	25.2604i	0.824343	−	1.42780i	0.902421	−	0.430856i	$-0.141788\pi$
$314$	16.6086	−	4.28498i	0.937278	−	0.241815i
$315$		0			0
$316$	21.3379	−	11.7954i	1.20035	−	0.663542i
$317$	−15.1594	−	8.75226i	−0.851435	−	0.491576i	0.00969989	−	0.999953i	$-0.496912\pi$
$317$	−15.1594	−	8.75226i	−0.851435	−	0.491576i	−0.861135	+	0.508377i	$0.830246\pi$
$318$		0			0
$319$	5.24298	+	9.08111i	0.293551	+	0.508445i
$320$	−2.96634	+	4.53307i	−0.165824	+	0.253407i
$321$		0			0
$322$	0.934526	−	0.201812i	0.0520791	−	0.0112466i
$323$		−	16.2369i		−	0.903447i
$324$		0			0
$325$	−5.03617	+	2.90763i	−0.279356	+	0.161286i
$326$	20.2392	+	20.6196i	1.12095	+	1.14201i
$327$		0			0
$328$	−12.4985	−	13.2168i	−0.690114	−	0.729773i
$329$	22.1753	−	11.6518i	1.22256	−	0.642386i
$330$		0			0
$331$	−1.01090	−	0.583642i	−0.0555640	−	0.0320799i	0.471961	−	0.881620i	$-0.343546\pi$
$331$	−1.01090	−	0.583642i	−0.0555640	−	0.0320799i	−0.527525	+	0.849540i	$0.676880\pi$
$332$	7.87602	−	13.0734i	0.432253	−	0.717498i
$333$		0			0
$334$	8.05011	+	2.23753i	0.440483	+	0.122432i
$335$	−10.6807			−0.583552
$336$		0			0
$337$	−14.0399			−0.764801			−0.382400	−	0.923997i	$-0.624903\pi$
$337$	−14.0399			−0.764801			−0.382400	+	0.923997i	$0.624903\pi$
$338$	−15.4791	−	4.30244i	−0.841954	−	0.234022i
$339$		0			0
$340$	−4.44859	+	7.38424i	−0.241259	+	0.400466i
$341$	6.20472	+	3.58230i	0.336004	+	0.193992i
$342$		0			0
$343$	−2.20639	+	18.3884i	−0.119134	+	0.992878i
$344$	−11.2782	+	10.6653i	−0.608081	+	0.575035i
$345$		0			0
$346$	−4.29638	−	4.37711i	−0.230975	−	0.235315i
$347$	−17.6542	+	10.1926i	−0.947725	+	0.547169i	−0.892373	−	0.451298i	$-0.850961\pi$
$347$	−17.6542	+	10.1926i	−0.947725	+	0.547169i	−0.0553515	+	0.998467i	$0.517628\pi$
$348$		0			0
$349$		−	16.5765i		−	0.887321i	−0.896195	−	0.443661i	$-0.853680\pi$
$349$		−	16.5765i		−	0.887321i	0.896195	−	0.443661i	$-0.146320\pi$
$350$	−5.19849	+	16.1778i	−0.277871	+	0.864739i
$351$		0			0
$352$	−6.36618	−	6.98814i	−0.339319	−	0.372469i
$353$	13.0736	+	22.6441i	0.695835	+	1.20522i	0.969898	+	0.243510i	$0.0782988\pi$
$353$	13.0736	+	22.6441i	0.695835	+	1.20522i	−0.274063	+	0.961712i	$0.588368\pi$
$354$		0			0
$355$	3.21780	+	1.85780i	0.170783	+	0.0986016i
$356$	11.9156	−	6.58682i	0.631525	−	0.349101i
$357$		0			0
$358$	−8.64428	+	2.23020i	−0.456865	+	0.117870i
$359$	−0.287276	+	0.497577i	−0.0151619	+	0.0262611i	−0.873507	−	0.486812i	$-0.838160\pi$
$359$	−0.287276	+	0.497577i	−0.0151619	+	0.0262611i	0.858345	+	0.513073i	$0.171493\pi$
$360$		0			0
$361$	−6.24652	−	10.8193i	−0.328764	−	0.569437i
$362$	−4.57009	+	16.4421i	−0.240199	+	0.864178i
$363$		0			0
$364$	6.05574	−	3.03946i	0.317407	−	0.159311i
$365$		−	1.94025i		−	0.101557i
$366$		0			0
$367$	9.75576	+	16.8975i	0.509247	+	0.882041i	0.999943	+	0.0107103i	$0.00340926\pi$
$367$	9.75576	+	16.8975i	0.509247	+	0.882041i	−0.490696	+	0.871331i	$0.663257\pi$
$368$	−1.02137	−	0.0380453i	−0.0532427	−	0.00198325i
$369$		0			0
$370$	−1.55340	−	6.02099i	−0.0807574	−	0.313016i
$371$	15.0124	+	0.597895i	0.779403	+	0.0310412i
$372$		0			0
$373$	−17.0833	−	9.86307i	−0.884542	−	0.510691i	−0.0123886	−	0.999923i	$-0.503944\pi$
$373$	−17.0833	−	9.86307i	−0.884542	−	0.510691i	−0.872153	+	0.489233i	$0.837277\pi$
$374$	−10.5375	−	10.7355i	−0.544880	−	0.555119i
$375$		0			0
$376$	−26.0506	+	6.20617i	−1.34346	+	0.320059i
$377$	8.03494			0.413820
$378$		0			0
$379$		−	10.5970i		−	0.544329i	−0.962251	−	0.272165i	$-0.912260\pi$
$379$		−	10.5970i		−	0.544329i	0.962251	−	0.272165i	$-0.0877395\pi$
$380$	0.0643102	−	3.45416i	0.00329904	−	0.177195i
$381$		0			0
$382$	8.03151	−	7.88337i	0.410928	−	0.403348i
$383$	9.60971	−	16.6445i	0.491033	−	0.850494i	−0.508913	−	0.860818i	$-0.669953\pi$
$383$	9.60971	−	16.6445i	0.491033	−	0.850494i	0.999947	+	0.0103232i	$0.00328603\pi$
$384$		0			0
$385$	2.53124	+	1.59899i	0.129004	+	0.0814922i
$386$	2.16969	+	8.40972i	0.110434	+	0.428043i
$387$		0			0
$388$	−0.818690	−	0.493215i	−0.0415627	−	0.0250392i
$389$	−22.0860	+	12.7513i	−1.11980	+	0.646519i	−0.941351	−	0.337429i	$-0.890443\pi$
$389$	−22.0860	+	12.7513i	−1.11980	+	0.646519i	−0.178453	+	0.983948i	$0.557109\pi$
$390$		0			0
$391$	−1.62645			−0.0822529
$392$	7.14734	−	18.4639i	0.360995	−	0.932568i
$393$		0			0
$394$	−5.74271	+	20.6609i	−0.289313	+	1.04088i
$395$	7.14911	−	4.12754i	0.359711	−	0.207679i
$396$		0			0
$397$	−27.7354	−	16.0130i	−1.39200	−	0.803671i	−0.398462	−	0.917185i	$-0.630456\pi$
$397$	−27.7354	−	16.0130i	−1.39200	−	0.803671i	−0.993536	+	0.113514i	$0.963789\pi$
$398$	−4.96461	−	19.2429i	−0.248854	−	0.964558i
$399$		0			0
$400$	9.66218	−	15.3830i	0.483109	−	0.769150i
$401$	−11.9637	+	20.7217i	−0.597437	+	1.03479i	0.395761	+	0.918354i	$0.370481\pi$
$401$	−11.9637	+	20.7217i	−0.597437	+	1.03479i	−0.993198	+	0.116438i	$0.962852\pi$
$402$		0			0
$403$	4.75441	−	2.74496i	0.236834	−	0.136736i
$404$	−26.3598	−	0.490771i	−1.31145	−	0.0244167i
$405$		0			0
$406$	17.3968	−	15.7667i	0.863390	−	0.782490i
$407$	10.8505			0.537839
$408$		0			0
$409$	−6.45748	−	11.1847i	−0.319302	−	0.553047i	0.661041	−	0.750350i	$-0.270115\pi$
$409$	−6.45748	−	11.1847i	−0.319302	−	0.553047i	−0.980343	+	0.197303i	$0.936782\pi$
$410$	−4.31438	−	4.39546i	−0.213072	−	0.217076i
$411$		0			0
$412$	−2.83108	+	1.56499i	−0.139477	+	0.0771018i
$413$	−26.6824	−	1.06268i	−1.31295	−	0.0522908i
$414$		0			0
$415$	2.58385	−	4.47536i	0.126836	−	0.219687i
$416$	−7.07637	+	1.54723i	−0.346948	+	0.0758591i
$417$		0			0
$418$	5.80827	+	1.61441i	0.284092	+	0.0789635i
$419$			32.2474i			1.57539i	0.616066	+	0.787694i	$0.288725\pi$
$419$			32.2474i			1.57539i	−0.616066	+	0.787694i	$0.711275\pi$
$420$		0			0
$421$			28.8215i			1.40468i	0.711844	+	0.702338i	$0.247860\pi$
$421$			28.8215i			1.40468i	−0.711844	+	0.702338i	$0.752140\pi$
$422$	−3.89450	+	14.0115i	−0.189581	+	0.682069i
$423$		0			0
$424$	−15.3922	−	4.58859i	−0.747511	−	0.222842i
$425$	14.4537	−	25.0345i	0.701106	−	1.21435i
$426$		0			0
$427$	18.7630	+	35.7090i	0.908005	+	1.72808i
$428$	−10.7826	−	19.5058i	−0.521197	−	0.942848i
$429$		0			0
$430$	−3.75076	+	3.68158i	−0.180878	+	0.177542i
$431$	−3.74266	−	6.48247i	−0.180277	−	0.312250i	0.761698	−	0.647933i	$-0.224366\pi$
$431$	−3.74266	−	6.48247i	−0.180277	−	0.312250i	−0.941975	+	0.335683i	$0.891033\pi$
$432$		0			0
$433$	5.02754			0.241608			0.120804	−	0.992676i	$-0.461453\pi$
$433$	5.02754			0.241608			0.120804	+	0.992676i	$0.461453\pi$
$434$	4.90764	−	15.2727i	0.235574	−	0.733112i
$435$		0			0
$436$	−8.07248	−	0.150295i	−0.386601	−	0.00719781i
$437$	0.564475	−	0.325900i	0.0270025	−	0.0155899i
$438$		0			0
$439$	17.3143	−	29.9892i	0.826365	−	1.43131i	−0.0745068	−	0.997221i	$-0.523738\pi$
$439$	17.3143	−	29.9892i	0.826365	−	1.43131i	0.900872	−	0.434086i	$-0.142928\pi$
$440$	−2.19917	−	2.32555i	−0.104841	−	0.110866i
$441$		0			0
$442$	−11.1613	+	2.87957i	−0.530887	+	0.136967i
$443$	5.45067	+	3.14695i	0.258969	+	0.149516i	0.623864	−	0.781533i	$-0.285562\pi$
$443$	5.45067	+	3.14695i	0.258969	+	0.149516i	−0.364895	+	0.931049i	$0.618895\pi$
$444$		0			0
$445$	3.99224	−	2.30492i	0.189250	−	0.109264i
$446$	−13.0233	−	3.61984i	−0.616672	−	0.171404i
$447$		0			0
$448$	−12.2853	+	17.2357i	−0.580427	+	0.814312i
$449$	−1.86843			−0.0881767			−0.0440883	−	0.999028i	$-0.514038\pi$
$449$	−1.86843			−0.0881767			−0.0440883	+	0.999028i	$0.514038\pi$
$450$		0			0
$451$	9.30750	−	5.37369i	0.438273	−	0.253037i
$452$	−34.8661	−	21.0049i	−1.63996	−	0.987987i
$453$		0			0
$454$	−37.4960	+	9.67388i	−1.75978	+	0.454018i
$455$	2.03088	−	1.06711i	0.0952090	−	0.0500268i
$456$		0			0
$457$	12.4603	−	21.5819i	0.582868	−	1.00956i	−0.412270	−	0.911062i	$-0.635264\pi$
$457$	12.4603	−	21.5819i	0.582868	−	1.00956i	0.995138	−	0.0984951i	$-0.0314029\pi$
$458$	−11.7122	−	11.9323i	−0.547275	−	0.557559i
$459$		0			0
$460$	−0.346002	−	0.00644192i	−0.0161324	−	0.000300356i
$461$			5.04894i			0.235153i	0.993064	+	0.117576i	$0.0375125\pi$
$461$			5.04894i			0.235153i	−0.993064	+	0.117576i	$0.962488\pi$
$462$		0			0
$463$	−14.4016			−0.669298			−0.334649	−	0.942343i	$-0.608618\pi$
$463$	−14.4016			−0.669298			−0.334649	+	0.942343i	$0.608618\pi$
$464$	−22.1889	+	11.7320i	−1.03010	+	0.544643i
$465$		0			0
$466$	−9.73128	+	9.55178i	−0.450793	+	0.442478i
$467$	26.9344	+	15.5506i	1.24637	+	0.719595i	0.970384	−	0.241566i	$-0.0776610\pi$
$467$	26.9344	+	15.5506i	1.24637	+	0.719595i	0.275990	+	0.961160i	$0.410994\pi$
$468$		0			0
$469$	−41.6973	−	1.66067i	−1.92540	−	0.0766827i
$470$	−8.77974	+	2.26515i	−0.404979	+	0.104484i
$471$		0			0
$472$	27.3575	+	8.15559i	1.25923	+	0.375391i
$473$	−4.58552	−	7.94235i	−0.210842	−	0.365189i
$474$		0			0
$475$			11.5846i			0.531539i
$476$	−18.5153	+	28.1361i	−0.848646	+	1.28962i
$477$		0			0
$478$	20.3883	+	5.66695i	0.932541	+	0.259200i
$479$	14.3914	+	24.9267i	0.657561	+	1.13893i	0.981245	+	0.192764i	$0.0617453\pi$
$479$	14.3914	+	24.9267i	0.657561	+	1.13893i	−0.323684	+	0.946165i	$0.604921\pi$
$480$		0			0
$481$	4.15713	−	7.20036i	0.189549	−	0.328308i
$482$	4.01722	+	15.5708i	0.182980	+	0.709230i
$483$		0			0
$484$	−14.3660	+	7.94138i	−0.653000	+	0.360972i
$485$	−0.280258	−	0.161807i	−0.0127258	−	0.00734727i
$486$		0			0
$487$	3.12575	+	5.41395i	0.141641	+	0.245330i	0.928115	−	0.372294i	$-0.121429\pi$
$487$	3.12575	+	5.41395i	0.141641	+	0.245330i	−0.786474	+	0.617624i	$0.788095\pi$
$488$	−9.99384	−	41.9495i	−0.452400	−	1.89897i
$489$		0			0
$490$	2.30320	−	6.29558i	0.104048	−	0.284405i
$491$		−	5.41504i		−	0.244377i	−0.992507	−	0.122189i	$-0.961009\pi$
$491$		−	5.41504i		−	0.244377i	0.992507	−	0.122189i	$-0.0389913\pi$
$492$		0			0
$493$	−34.5901	+	19.9706i	−1.55786	+	0.899430i
$494$	3.29663	−	3.23582i	0.148322	−	0.145587i
$495$		0			0
$496$	−9.12160	+	14.5224i	−0.409572	+	0.652073i
$497$	12.2733	+	7.75309i	0.550533	+	0.347773i
$498$		0			0
$499$	−7.92389	−	4.57486i	−0.354722	−	0.204799i	0.312041	−	0.950069i	$-0.398987\pi$
$499$	−7.92389	−	4.57486i	−0.354722	−	0.204799i	−0.666763	+	0.745270i	$0.732321\pi$
$500$	6.66840	−	11.0689i	0.298220	−	0.495016i
$501$		0			0
$502$	−1.42286	+	5.11913i	−0.0635056	+	0.228478i
$503$	0.361250			0.0161073			0.00805366	−	0.999968i	$-0.497436\pi$
$503$	0.361250			0.0161073			0.00805366	+	0.999968i	$0.497436\pi$
$504$		0			0
$505$	−8.92659			−0.397228
$506$	0.161715	−	0.581812i	0.00718911	−	0.0258647i
$507$		0			0
$508$	−26.3791	−	15.8919i	−1.17038	−	0.705090i
$509$	28.3684	+	16.3785i	1.25741	+	0.725965i	0.972570	−	0.232610i	$-0.0747267\pi$
$509$	28.3684	+	16.3785i	1.25741	+	0.725965i	0.284838	+	0.958576i	$0.408060\pi$
$510$		0			0
$511$	0.301676	−	7.57468i	0.0133453	−	0.335084i
$512$	17.2827	−	14.6051i	0.763794	−	0.645461i
$513$		0			0
$514$	10.0868	−	9.90072i	0.444909	−	0.436702i
$515$	−0.948535	+	0.547637i	−0.0417975	+	0.0241318i
$516$		0			0
$517$		−	15.8221i		−	0.695854i
$518$	−5.12826	−	23.7473i	−0.225323	−	1.04339i
$519$		0			0
$520$	−2.38579	+	0.568379i	−0.104624	+	0.0249251i
$521$	−10.2681	−	17.7848i	−0.449852	−	0.779166i	0.548524	−	0.836135i	$-0.315190\pi$
$521$	−10.2681	−	17.7848i	−0.449852	−	0.779166i	−0.998376	+	0.0569688i	$0.981856\pi$
$522$		0			0
$523$	−11.2213	−	6.47863i	−0.490674	−	0.283291i	0.234180	−	0.972193i	$-0.424760\pi$
$523$	−11.2213	−	6.47863i	−0.490674	−	0.283291i	−0.724854	+	0.688902i	$0.758093\pi$
$524$	2.20102	+	3.98165i	0.0961518	+	0.173939i
$525$		0			0
$526$	5.34069	+	20.7006i	0.232865	+	0.902587i
$527$	−13.6450	+	23.6339i	−0.594386	+	1.02951i
$528$		0			0
$529$	11.4674	+	19.8620i	0.498581	+	0.863567i
$530$	−5.23960	−	1.45635i	−0.227594	−	0.0632599i
$531$		0			0
$532$	0.788127	−	13.4749i	0.0341696	−	0.584212i
$533$		−	8.23524i		−	0.356708i
$534$		0			0
$535$	−3.77315	−	6.53529i	−0.163127	−	0.282545i
$536$	42.7523	+	12.7450i	1.84662	+	0.550498i
$537$		0			0
$538$	12.9284	−	3.33549i	0.557383	−	0.143803i
$539$	9.63327	+	6.63598i	0.414934	+	0.285832i
$540$		0			0
$541$	26.6933	+	15.4114i	1.14763	+	0.662586i	0.948309	−	0.317347i	$-0.102792\pi$
$541$	26.6933	+	15.4114i	1.14763	+	0.662586i	0.199324	+	0.979934i	$0.436125\pi$
$542$	17.0168	−	16.7030i	0.730936	−	0.717454i
$543$		0			0
$544$	26.6179	−	24.2489i	1.14123	−	1.03966i
$545$	−2.73370			−0.117099
$546$		0			0
$547$			12.7122i			0.543537i	0.962363	+	0.271768i	$0.0876084\pi$
$547$			12.7122i			0.543537i	−0.962363	+	0.271768i	$0.912392\pi$
$548$	0.254665	−	13.6783i	0.0108787	−	0.584307i
$549$		0			0
$550$	7.51823	+	7.65950i	0.320578	+	0.326602i
$551$	8.00323	−	13.8620i	0.340949	−	0.590541i
$552$		0			0
$553$	28.5517	−	15.0022i	1.21414	−	0.637959i
$554$	−12.3007	+	3.17356i	−0.522608	+	0.134832i
$555$		0			0
$556$	7.90146	−	13.1157i	0.335097	−	0.556228i
$557$	9.04134	−	5.22002i	0.383094	−	0.221179i	−0.296070	−	0.955166i	$-0.595676\pi$
$557$	9.04134	−	5.22002i	0.383094	−	0.221179i	0.679164	+	0.733987i	$0.262343\pi$
$558$		0			0
$559$	−7.02736			−0.297226
$560$	−4.05028	+	5.91220i	−0.171156	+	0.249836i
$561$		0			0
$562$	30.9006	+	8.58885i	1.30346	+	0.362299i
$563$	−11.7680	+	6.79424i	−0.495961	+	0.286343i	−0.727044	−	0.686591i	$-0.759106\pi$
$563$	−11.7680	+	6.79424i	−0.495961	+	0.286343i	0.231083	+	0.972934i	$0.425773\pi$
$564$		0			0
$565$	−11.9355	−	6.89098i	−0.502131	−	0.289906i
$566$	−25.4376	+	6.56284i	−1.06922	+	0.275857i
$567$		0			0
$568$	−10.6632	−	11.2760i	−0.447417	−	0.473129i
$569$	8.55098	−	14.8107i	0.358476	−	0.620898i	−0.629231	−	0.777219i	$-0.716630\pi$
$569$	8.55098	−	14.8107i	0.358476	−	0.620898i	0.987706	+	0.156321i	$0.0499633\pi$
$570$		0			0
$571$	−0.502264	+	0.289982i	−0.0210191	+	0.0121354i	−0.510473	−	0.859894i	$-0.670530\pi$
$571$	−0.502264	+	0.289982i	−0.0210191	+	0.0121354i	0.489454	+	0.872029i	$0.337196\pi$
$572$	0.0796655	−	4.27891i	0.00333098	−	0.178910i
$573$		0			0
$574$	−16.1598	−	17.8305i	−0.674496	−	0.744232i
$575$	1.16043			0.0483932
$576$		0			0
$577$	8.40341	+	14.5551i	0.349838	+	0.605938i	0.986221	−	0.165436i	$-0.0529031\pi$
$577$	8.40341	+	14.5551i	0.349838	+	0.605938i	−0.636382	+	0.771374i	$0.719570\pi$
$578$	23.7342	−	23.2964i	0.987211	−	0.969002i
$579$		0			0
$580$	−7.43762	+	4.11144i	−0.308830	+	0.170718i
$581$	10.7831	−	17.0699i	0.447358	−	0.708178i
$582$		0			0
$583$	4.74478	−	8.21820i	0.196509	−	0.340363i
$584$	−2.31523	+	7.76633i	−0.0958051	+	0.321373i
$585$		0			0
$586$	−5.89373	+	21.2042i	−0.243468	+	0.875939i
$587$			25.3598i			1.04671i	0.852114	+	0.523356i	$0.175320\pi$
$587$			25.3598i			1.04671i	−0.852114	+	0.523356i	$0.824680\pi$
$588$		0			0
$589$		−	10.9365i		−	0.450630i
$590$	9.31266	+	2.58846i	0.383396	+	0.106565i
$591$		0			0
$592$	−0.966771	+	25.9541i	−0.0397341	+	1.06671i
$593$	−5.02137	+	8.69726i	−0.206203	+	0.357154i	−0.950515	−	0.310678i	$-0.899444\pi$
$593$	−5.02137	+	8.69726i	−0.206203	+	0.357154i	0.744312	+	0.667832i	$0.232777\pi$
$594$		0			0
$595$	−6.09059	+	9.64154i	−0.249690	+	0.395265i
$596$	13.0204	+	23.5540i	0.533337	+	0.964809i
$597$		0			0
$598$	−0.324131	−	0.330222i	−0.0132547	−	0.0135038i
$599$	1.71260	+	2.96631i	0.0699750	+	0.121200i	0.898890	−	0.438174i	$-0.144375\pi$
$599$	1.71260	+	2.96631i	0.0699750	+	0.121200i	−0.828915	+	0.559374i	$0.811041\pi$
$600$		0			0
$601$	0.842886			0.0343820			0.0171910	−	0.999852i	$-0.494528\pi$
$601$	0.842886			0.0343820			0.0171910	+	0.999852i	$0.494528\pi$
$602$	−15.2153	+	13.7896i	−0.620128	+	0.562022i
$603$		0			0
$604$	0.590259	−	31.7034i	0.0240173	−	1.28999i
$605$	−4.81323	+	2.77892i	−0.195686	+	0.112979i
$606$		0			0
$607$	2.64017	−	4.57291i	0.107161	−	0.185609i	−0.807458	−	0.589925i	$-0.799157\pi$
$607$	2.64017	−	4.57291i	0.107161	−	0.185609i	0.914619	+	0.404316i	$0.132491\pi$
$608$	−4.37915	+	13.7494i	−0.177598	+	0.557611i
$609$		0			0
$610$	−3.64759	−	14.1381i	−0.147686	−	0.572434i
$611$	−10.4995	−	6.06188i	−0.424764	−	0.245237i
$612$		0			0
$613$	27.2280	−	15.7201i	1.09973	−	0.634928i	0.163578	−	0.986530i	$-0.447696\pi$
$613$	27.2280	−	15.7201i	1.09973	−	0.634928i	0.936149	+	0.351602i	$0.114363\pi$
$614$	10.9188	−	39.2831i	0.440645	−	1.58534i
$615$		0			0
$616$	−8.22390	−	9.42080i	−0.331350	−	0.379575i
$617$	37.2297			1.49881			0.749406	−	0.662110i	$-0.230339\pi$
$617$	37.2297			1.49881			0.749406	+	0.662110i	$0.230339\pi$
$618$		0			0
$619$	28.2967	−	16.3371i	1.13734	−	0.656644i	0.191570	−	0.981479i	$-0.438642\pi$
$619$	28.2967	−	16.3371i	1.13734	−	0.656644i	0.945771	+	0.324835i	$0.105309\pi$
$620$	−2.99638	+	4.97370i	−0.120338	+	0.199749i
$621$		0			0
$622$	4.26382	+	16.5266i	0.170963	+	0.662656i
$623$	15.9439	−	8.37760i	0.638780	−	0.335642i
$624$		0			0
$625$	−9.16593	+	15.8758i	−0.366637	+	0.635034i
$626$	−29.4385	+	28.8955i	−1.17660	+	1.15489i
$627$		0			0
$628$	−24.2531	−	0.451547i	−0.967802	−	0.0180187i
$629$			41.3297i			1.64792i
$630$		0			0
$631$	3.95431			0.157418			0.0787092	−	0.996898i	$-0.474920\pi$
$631$	3.95431			0.157418			0.0787092	+	0.996898i	$0.474920\pi$
$632$	−33.5413	+	7.99072i	−1.33420	+	0.317854i
$633$		0			0
$634$	17.3408	+	17.6667i	0.688693	+	0.701634i
$635$	−9.03020	−	5.21359i	−0.358352	−	0.206895i
$636$		0			0
$637$	8.09439	−	3.85018i	0.320712	−	0.152550i
$638$	−3.70464	−	14.3592i	−0.146668	−	0.568486i
$639$		0			0
$640$	5.75861	−	5.05316i	0.227629	−	0.199744i
$641$	−10.8258	−	18.7508i	−0.427593	−	0.740612i	0.569066	−	0.822292i	$-0.307305\pi$
$641$	−10.8258	−	18.7508i	−0.427593	−	0.740612i	−0.996659	+	0.0816797i	$0.973972\pi$
$642$		0			0
$643$			5.48021i			0.216118i	0.994144	+	0.108059i	$0.0344636\pi$
$643$			5.48021i			0.216118i	−0.994144	+	0.108059i	$0.965536\pi$
$644$	−1.34978	−	0.0789464i	−0.0531887	−	0.00311092i
$645$		0			0
$646$	−6.14932	+	22.1238i	−0.241942	+	0.870448i
$647$	15.5285	+	26.8961i	0.610487	+	1.05739i	0.991158	+	0.132684i	$0.0423594\pi$
$647$	15.5285	+	26.8961i	0.610487	+	1.05739i	−0.380672	+	0.924710i	$0.624307\pi$
$648$		0			0
$649$	−8.43319	+	14.6067i	−0.331032	+	0.573364i
$650$	7.96327	−	2.05450i	0.312345	−	0.0805843i
$651$		0			0
$652$	−19.7680	−	35.7605i	−0.774176	−	1.40049i
$653$	10.6381	+	6.14194i	0.416303	+	0.240353i	0.693494	−	0.720462i	$-0.256070\pi$
$653$	10.6381	+	6.14194i	0.416303	+	0.240353i	−0.277191	+	0.960815i	$0.589404\pi$
$654$		0			0
$655$	0.770199	+	1.33402i	0.0300942	+	0.0521246i
$656$	12.0244	+	22.7421i	0.469475	+	0.887930i
$657$		0			0
$658$	−34.6280	+	7.47797i	−1.34994	+	0.291522i
$659$		−	12.8321i		−	0.499869i	−0.968263	−	0.249934i	$-0.919591\pi$
$659$		−	12.8321i		−	0.499869i	0.968263	−	0.249934i	$-0.0804091\pi$
$660$		0			0
$661$	−11.1865	+	6.45853i	−0.435104	+	0.251208i	−0.701519	−	0.712651i	$-0.747494\pi$
$661$	−11.1865	+	6.45853i	−0.435104	+	0.251208i	0.266415	+	0.963859i	$0.414161\pi$
$662$	1.15637	+	1.17810i	0.0449435	+	0.0457881i
$663$		0			0
$664$	−15.6828	+	14.8305i	−0.608609	+	0.575535i
$665$	0.181873	−	4.56660i	0.00705274	−	0.177085i
$666$		0			0
$667$	−1.38855	−	0.801680i	−0.0537649	−	0.0310412i
$668$	−10.1213	−	6.09755i	−0.391607	−	0.235921i
$669$		0			0
$670$	14.5532	+	4.04506i	0.562237	+	0.156274i
$671$	25.4784			0.983582
$672$		0			0
$673$	3.52699			0.135955			0.0679777	−	0.997687i	$-0.478345\pi$
$673$	3.52699			0.135955			0.0679777	+	0.997687i	$0.478345\pi$
$674$	19.1302	+	5.31724i	0.736866	+	0.204813i
$675$		0			0
$676$	19.4618	+	11.7247i	0.748531	+	0.450948i
$677$	−36.2777	−	20.9449i	−1.39427	−	0.804979i	−0.400481	−	0.916305i	$-0.631157\pi$
$677$	−36.2777	−	20.9449i	−1.39427	−	0.804979i	−0.993784	+	0.111326i	$0.964490\pi$
$678$		0			0
$679$	−1.06896	−	0.675263i	−0.0410228	−	0.0259142i
$680$	8.85806	−	8.37667i	0.339691	−	0.321231i
$681$		0			0
$682$	−7.09760	−	7.23097i	−0.271781	−	0.276888i
$683$	3.08116	−	1.77891i	0.117897	−	0.0680680i	−0.439892	−	0.898051i	$-0.644983\pi$
$683$	3.08116	−	1.77891i	0.117897	−	0.0680680i	0.557789	+	0.829983i	$0.311650\pi$
$684$		0			0
$685$		−	4.63208i		−	0.176983i
$686$	9.97046	−	24.2196i	0.380674	−	0.924709i
$687$		0			0
$688$	19.4065	−	10.2608i	0.739864	−	0.391189i
$689$	−3.63572	−	6.29725i	−0.138510	−	0.239906i
$690$		0			0
$691$	−3.16904	−	1.82965i	−0.120556	−	0.0696031i	0.438509	−	0.898727i	$-0.355507\pi$
$691$	−3.16904	−	1.82965i	−0.120556	−	0.0696031i	−0.559065	+	0.829124i	$0.688840\pi$
$692$	4.19635	+	7.59122i	0.159521	+	0.288575i
$693$		0			0
$694$	27.9150	−	7.20201i	1.05964	−	0.273384i
$695$	2.59220	−	4.48981i	0.0983276	−	0.170308i
$696$		0			0
$697$	20.4685	+	35.4524i	0.775298	+	1.34286i
$698$	−6.27794	+	22.5865i	−0.237623	+	0.854912i
$699$		0			0
$700$	13.2102	−	20.0744i	0.499298	−	0.758741i
$701$			12.8715i			0.486151i	0.970007	+	0.243076i	$0.0781563\pi$
$701$			12.8715i			0.486151i	−0.970007	+	0.243076i	$0.921844\pi$
$702$		0			0
$703$	−8.28145	−	14.3439i	−0.312341	−	0.540990i
$704$	6.02772	+	11.9328i	0.227178	+	0.449734i
$705$		0			0
$706$	−9.23763	−	35.8051i	−0.347663	−	1.34754i
$707$	−34.8491	−	1.38793i	−1.31064	−	0.0521985i
$708$		0			0
$709$	35.6931	+	20.6074i	1.34048	+	0.773929i	0.986878	−	0.161466i	$-0.0516221\pi$
$709$	35.6931	+	20.6074i	1.34048	+	0.773929i	0.353606	+	0.935395i	$0.384955\pi$
$710$	−3.68085	−	3.75002i	−0.138140	−	0.140736i
$711$		0			0
$712$	−18.7303	+	4.46221i	−0.701947	+	0.167228i
$713$	−1.09550			−0.0410270
$714$		0			0
$715$		−	1.44903i		−	0.0541907i
$716$	12.6230	+	0.235017i	0.471743	+	0.00878299i
$717$		0			0
$718$	0.579875	−	0.569180i	0.0216408	−	0.0212416i
$719$	−14.3208	+	24.8044i	−0.534078	+	0.925049i	0.465130	+	0.885242i	$0.346008\pi$
$719$	−14.3208	+	24.8044i	−0.534078	+	0.925049i	−0.999207	+	0.0398069i	$0.987326\pi$
$720$		0			0
$721$	−3.78820	+	1.99048i	−0.141080	+	0.0741292i
$722$	4.41373	+	17.1076i	0.164262	+	0.636680i
$723$		0			0
$724$	12.4540	−	20.6725i	0.462851	−	0.768289i
$725$	24.6791	−	14.2485i	0.916561	−	0.529177i
$726$		0			0
$727$	−47.0440			−1.74476			−0.872382	−	0.488825i	$-0.837426\pi$
$727$	−47.0440			−1.74476			−0.872382	+	0.488825i	$0.837426\pi$
$728$	−9.40243	+	1.84798i	−0.348477	+	0.0684908i
$729$		0			0
$730$	−0.734821	+	2.64371i	−0.0271969	+	0.0978481i
$731$	30.2525	−	17.4663i	1.11893	−	0.646014i
$732$		0			0
$733$	7.60577	+	4.39119i	0.280926	+	0.162192i	0.633842	−	0.773462i	$-0.281477\pi$
$733$	7.60577	+	4.39119i	0.280926	+	0.162192i	−0.352917	+	0.935655i	$0.614810\pi$
$734$	−6.89332	−	26.7186i	−0.254437	−	0.986200i
$735$		0			0
$736$	1.37727	+	0.438657i	0.0507669	+	0.0161691i
$737$	−13.1788	+	22.8263i	−0.485446	+	0.840818i
$738$		0			0
$739$	21.6962	−	12.5263i	0.798106	−	0.460787i	−0.0447026	−	0.999000i	$-0.514234\pi$
$739$	21.6962	−	12.5263i	0.798106	−	0.460787i	0.842808	+	0.538214i	$0.180901\pi$
$740$	−0.163696	+	8.79227i	−0.00601758	+	0.323210i
$741$		0			0
$742$	−20.2288	−	6.50021i	−0.742622	−	0.238630i
$743$	10.2336			0.375433			0.187717	−	0.982223i	$-0.439891\pi$
$743$	10.2336			0.375433			0.187717	+	0.982223i	$0.439891\pi$
$744$		0			0
$745$	4.55622	+	7.89160i	0.166927	+	0.289126i
$746$	19.5417	+	19.9089i	0.715472	+	0.728917i
$747$		0			0
$748$	10.2922	+	18.6186i	0.376318	+	0.680762i
$749$	−13.7141	−	26.1002i	−0.501103	−	0.953680i
$750$		0			0
$751$	−16.1843	+	28.0320i	−0.590573	+	1.02290i	0.403583	+	0.914943i	$0.367765\pi$
$751$	−16.1843	+	28.0320i	−0.590573	+	1.02290i	−0.994155	+	0.107959i	$0.965569\pi$
$752$	37.8460	+	1.40973i	1.38010	+	0.0514077i
$753$		0			0
$754$	−10.9481	−	3.04303i	−0.398705	−	0.110820i
$755$		−	10.7362i		−	0.390730i
$756$		0			0
$757$		−	5.13921i		−	0.186788i	−0.995629	−	0.0933940i	$-0.970228\pi$
$757$		−	5.13921i		−	0.186788i	0.995629	−	0.0933940i	$-0.0297716\pi$
$758$	−4.01333	+	14.4390i	−0.145771	+	0.524448i
$759$		0			0
$760$	−1.39580	+	4.68214i	−0.0506310	+	0.169839i
$761$	8.46993	−	14.6704i	0.307035	−	0.531800i	−0.670677	−	0.741749i	$-0.733997\pi$
$761$	8.46993	−	14.6704i	0.307035	−	0.531800i	0.977712	+	0.209949i	$0.0673299\pi$
$762$		0			0
$763$	−10.6723	−	0.425043i	−0.386362	−	0.0153876i
$764$	−13.9290	+	7.69983i	−0.503935	+	0.278570i
$765$		0			0
$766$	−19.3975	+	19.0397i	−0.700859	+	0.687932i
$767$	6.46198	+	11.1925i	0.233329	+	0.404137i
$768$		0			0
$769$	−22.2421			−0.802071			−0.401036	−	0.916062i	$-0.631350\pi$
$769$	−22.2421			−0.802071			−0.401036	+	0.916062i	$0.631350\pi$
$770$	−2.84339	−	3.13737i	−0.102469	−	0.113063i
$771$		0			0
$772$	0.228639	−	12.2804i	0.00822892	−	0.441983i
$773$	−38.1492	+	22.0255i	−1.37213	+	0.792201i	−0.991196	−	0.132400i	$-0.957732\pi$
$773$	−38.1492	+	22.0255i	−1.37213	+	0.792201i	−0.380936	+	0.924601i	$0.624398\pi$
$774$		0			0
$775$	9.73537	−	16.8622i	0.349705	−	0.605707i
$776$	0.928721	+	0.982093i	0.0333391	+	0.0352551i
$777$		0			0
$778$	34.9227	−	9.00997i	1.25204	−	0.323023i
$779$	−14.2076	−	8.20274i	−0.509039	−	0.293894i
$780$		0			0
$781$	7.94076	−	4.58460i	0.284143	−	0.164050i
$782$	2.21613	+	0.615975i	0.0792486	+	0.0220272i
$783$		0			0
$784$	−16.7314	+	22.4513i	−0.597550	+	0.801831i
$785$	−8.21317			−0.293140
$786$		0			0
$787$	21.7752	−	12.5719i	0.776202	−	0.448140i	−0.0588808	−	0.998265i	$-0.518753\pi$
$787$	21.7752	−	12.5719i	0.776202	−	0.448140i	0.835082	+	0.550125i	$0.185420\pi$
$788$	15.6496	−	25.9768i	0.557492	−	0.925384i
$789$		0			0
$790$	−11.3043	+	2.91648i	−0.402189	+	0.103764i
$791$	−45.5244	−	28.7579i	−1.61866	−	1.02251i
$792$		0			0
$793$	9.76148	−	16.9074i	0.346640	−	0.600399i
$794$	31.7266	+	32.3228i	1.12593	+	1.14709i
$795$		0			0
$796$	−0.523166	+	28.0998i	−0.0185431	+	0.995970i
$797$		−	55.0759i		−	1.95089i	−0.220247	−	0.975444i	$-0.570686\pi$
$797$		−	55.0759i		−	1.95089i	0.220247	−	0.975444i	$-0.429314\pi$
$798$		0			0
$799$	60.2665			2.13207
$800$	−18.9912	+	17.3010i	−0.671441	+	0.611681i
$801$		0			0
$802$	24.1490	−	23.7036i	0.852732	−	0.837003i
$803$	−4.14660	−	2.39404i	−0.146330	−	0.0844839i
$804$		0			0
$805$	−0.457434	−	0.0182182i	−0.0161224	−	0.000642106i
$806$	−7.51774	+	1.93956i	−0.264801	+	0.0683180i
$807$		0			0
$808$	35.7309	+	10.6518i	1.25701	+	0.374729i
$809$	−0.781329	−	1.35330i	−0.0274701	−	0.0475796i	0.851964	−	0.523601i	$-0.175412\pi$
$809$	−0.781329	−	1.35330i	−0.0274701	−	0.0475796i	−0.879434	+	0.476022i	$0.842078\pi$
$810$		0			0
$811$			24.5686i			0.862720i	0.902180	+	0.431360i	$0.141966\pi$
$811$			24.5686i			0.862720i	−0.902180	+	0.431360i	$0.858034\pi$
$812$	−29.6755	+	14.8945i	−1.04140	+	0.522695i
$813$		0			0
$814$	−14.7844	−	4.10935i	−0.518194	−	0.144033i
$815$	−6.91741	−	11.9813i	−0.242306	−	0.419687i
$816$		0			0
$817$	−6.99962	+	12.1237i	−0.244886	+	0.424155i
$818$	4.56279	+	17.6854i	0.159534	+	0.618356i
$819$		0			0
$820$	4.21394	+	7.62303i	0.147157	+	0.266208i
$821$	45.1801	+	26.0848i	1.57680	+	0.910365i	0.995302	+	0.0968147i	$0.0308654\pi$
$821$	45.1801	+	26.0848i	1.57680	+	0.910365i	0.581495	+	0.813550i	$0.302468\pi$
$822$		0			0
$823$	9.19076	+	15.9189i	0.320370	+	0.554897i	0.980564	−	0.196198i	$-0.0628595\pi$
$823$	9.19076	+	15.9189i	0.320370	+	0.554897i	−0.660195	+	0.751095i	$0.729526\pi$
$824$	4.45022	−	1.06020i	0.155031	−	0.0369337i
$825$		0			0
$826$	35.9539	+	11.5532i	1.25099	+	0.401988i
$827$		−	10.0002i		−	0.347742i	−0.984768	−	0.173871i	$-0.944372\pi$
$827$		−	10.0002i		−	0.347742i	0.984768	−	0.173871i	$-0.0556275\pi$
$828$		0			0
$829$	−33.3708	+	19.2666i	−1.15902	+	0.669158i	−0.951068	−	0.308982i	$-0.900012\pi$
$829$	−33.3708	+	19.2666i	−1.15902	+	0.669158i	−0.207948	+	0.978140i	$0.566679\pi$
$830$	−5.21557	+	5.11937i	−0.181035	+	0.177696i
$831$		0			0
$832$	10.2280	+	0.571806i	0.354590	+	0.0198238i
$833$	−25.2765	+	36.6933i	−0.875780	+	1.27135i
$834$		0			0
$835$	−3.46478	−	2.00039i	−0.119904	−	0.0692265i
$836$	−7.30269	−	4.39946i	−0.252569	−	0.152159i
$837$		0			0
$838$	12.2129	−	43.9390i	0.421887	−	1.51785i
$839$	−17.3005			−0.597279			−0.298640	−	0.954366i	$-0.596533\pi$
$839$	−17.3005			−0.597279			−0.298640	+	0.954366i	$0.596533\pi$
$840$		0			0
$841$	−10.3743			−0.357733
$842$	10.9154	−	39.2711i	0.376170	−	1.35337i
$843$		0			0
$844$	10.6130	−	17.6165i	0.365314	−	0.606386i
$845$	6.66225	+	3.84645i	0.229188	+	0.132322i
$846$		0			0
$847$	−19.2228	+	10.1004i	−0.660502	+	0.347055i
$848$	19.2350	+	12.0816i	0.660532	+	0.414885i
$849$		0			0
$850$	−29.1752	+	28.6370i	−1.00070	+	0.982242i
$851$	−1.43682	+	0.829549i	−0.0492536	+	0.0284366i
$852$		0			0
$853$			3.16642i			0.108416i	0.998530	+	0.0542080i	$0.0172634\pi$
$853$			3.16642i			0.108416i	−0.998530	+	0.0542080i	$0.982737\pi$
$854$	−12.0418	−	55.7617i	−0.412063	−	1.90813i
$855$		0			0
$856$	7.30463	+	30.6614i	0.249667	+	1.04799i
$857$	−5.20669	−	9.01825i	−0.177857	−	0.308058i	0.763289	−	0.646057i	$-0.223583\pi$
$857$	−5.20669	−	9.01825i	−0.177857	−	0.308058i	−0.941146	+	0.337999i	$0.890250\pi$
$858$		0			0
$859$	−30.4427	−	17.5761i	−1.03869	−	0.599689i	−0.119229	−	0.992867i	$-0.538042\pi$
$859$	−30.4427	−	17.5761i	−1.03869	−	0.599689i	−0.919463	+	0.393178i	$0.871376\pi$
$860$	6.50494	−	3.59587i	0.221817	−	0.122618i
$861$		0			0
$862$	2.64452	+	10.2502i	0.0900728	+	0.349123i
$863$	15.9590	−	27.6418i	0.543251	−	0.940939i	−0.455463	−	0.890255i	$-0.650526\pi$
$863$	15.9590	−	27.6418i	0.543251	−	0.940939i	0.998715	−	0.0506844i	$-0.0161403\pi$
$864$		0			0
$865$	1.46842	+	2.54339i	0.0499279	+	0.0864777i
$866$	−6.85032	−	1.90405i	−0.232783	−	0.0647023i
$867$		0			0
$868$	−12.4711	+	18.9513i	−0.423296	+	0.643248i
$869$		−	20.3716i		−	0.691059i
$870$		0			0
$871$	10.0983	+	17.4908i	0.342168	+	0.592653i
$872$	10.9423	+	3.26203i	0.370553	+	0.110466i
$873$		0			0
$874$	−0.892556	+	0.230277i	−0.0301912	+	0.00778924i
$875$	9.12973	−	14.4526i	0.308641	−	0.488587i
$876$		0			0
$877$	20.4800	+	11.8241i	0.691560	+	0.399272i	0.804196	−	0.594364i	$-0.202596\pi$
$877$	20.4800	+	11.8241i	0.691560	+	0.399272i	−0.112636	+	0.993636i	$0.535930\pi$
$878$	−34.9494	+	34.3047i	−1.17948	+	1.15773i
$879$		0			0
$880$	2.11576	+	4.00158i	0.0713222	+	0.134893i
$881$	−40.6718			−1.37027			−0.685134	−	0.728417i	$-0.740256\pi$
$881$	−40.6718			−1.37027			−0.685134	+	0.728417i	$0.740256\pi$
$882$		0			0
$883$		−	32.7233i		−	1.10123i	−0.834760	−	0.550613i	$-0.814394\pi$
$883$		−	32.7233i		−	1.10123i	0.834760	−	0.550613i	$-0.185606\pi$
$884$	16.2984	+	0.303447i	0.548176	+	0.0102060i
$885$		0			0
$886$	−6.23504	−	6.35220i	−0.209470	−	0.213406i
$887$	−7.92985	+	13.7349i	−0.266258	+	0.461173i	−0.967892	−	0.251365i	$-0.919121\pi$
$887$	−7.92985	+	13.7349i	−0.266258	+	0.461173i	0.701634	+	0.712537i	$0.252454\pi$
$888$		0			0
$889$	−34.4429	−	21.7577i	−1.15518	−	0.729730i
$890$	−6.31259	+	1.62863i	−0.211599	+	0.0545919i
$891$		0			0
$892$	16.3741	+	9.86450i	0.548246	+	0.330288i
$893$	−20.9161	+	12.0759i	−0.699930	+	0.404105i
$894$		0			0
$895$	4.27471			0.142888
$896$	23.2671	−	18.8320i	0.777298	−	0.629132i
$897$		0			0
$898$	2.54585	+	0.707620i	0.0849560	+	0.0236136i
$899$	−23.2984	+	13.4513i	−0.777045	+	0.448627i
$900$		0			0
$901$	31.3033	+	18.0729i	1.04286	+	0.602097i
$902$	−14.7172	+	3.79699i	−0.490028	+	0.126426i
$903$		0			0
$904$	39.5521	+	41.8250i	1.31548	+	1.39108i
$905$	4.08574	−	7.07671i	0.135815	−	0.235238i
$906$		0			0
$907$	−27.9075	+	16.1124i	−0.926652	+	0.535003i	−0.885751	−	0.464160i	$-0.846356\pi$
$907$	−27.9075	+	16.1124i	−0.926652	+	0.535003i	−0.0409010	+	0.999163i	$0.513023\pi$
$908$	54.7543	+	1.01942i	1.81709	+	0.0338308i
$909$		0			0
$910$	−3.17133	+	0.684854i	−0.105129	+	0.0227027i
$911$	−58.1634			−1.92704			−0.963520	−	0.267635i	$-0.913758\pi$
$911$	−58.1634			−1.92704			−0.963520	+	0.267635i	$0.913758\pi$
$912$		0			0
$913$	−6.37632	−	11.0441i	−0.211025	−	0.365507i
$914$	−25.1515	+	24.6876i	−0.831937	+	0.816592i
$915$		0			0
$916$	11.4395	+	20.6941i	0.377972	+	0.683754i
$917$	2.79941	+	5.32774i	0.0924448	+	0.175937i
$918$		0			0
$919$	−2.26347	+	3.92045i	−0.0746650	+	0.129324i	−0.900941	−	0.433943i	$-0.857122\pi$
$919$	−2.26347	+	3.92045i	−0.0746650	+	0.129324i	0.826276	+	0.563266i	$0.190455\pi$
$920$	0.469009	+	0.139817i	0.0154628	+	0.00460963i
$921$		0			0
$922$	1.91216	−	6.87948i	0.0629736	−	0.226564i
$923$		−	7.02596i		−	0.231262i
$924$		0			0
$925$		−	29.4877i		−	0.969549i
$926$	19.6230	+	5.45422i	0.644851	+	0.179237i
$927$		0			0
$928$	34.6769	−	7.58200i	1.13833	−	0.248891i
$929$	−8.89148	+	15.4005i	−0.291720	+	0.505274i	−0.974217	−	0.225615i	$-0.927561\pi$
$929$	−8.89148	+	15.4005i	−0.291720	+	0.505274i	0.682496	+	0.730889i	$0.260894\pi$
$930$		0			0
$931$	1.42005	−	17.7996i	0.0465404	−	0.583357i
$932$	16.8769	−	9.32940i	0.552822	−	0.305595i
$933$		0			0
$934$	−30.8103	−	31.3893i	−1.00814	−	1.02709i
$935$	3.60152	+	6.23802i	0.117782	+	0.204005i
$936$		0			0
$937$	2.28933			0.0747893			0.0373946	−	0.999301i	$-0.488094\pi$
$937$	2.28933			0.0747893			0.0373946	+	0.999301i	$0.488094\pi$
$938$	56.1861	+	18.0545i	1.83454	+	0.589501i
$939$		0			0
$940$	12.8208	+	0.238700i	0.418168	+	0.00778552i
$941$	41.5525	−	23.9904i	1.35457	−	0.782064i	0.365688	−	0.930738i	$-0.380834\pi$
$941$	41.5525	−	23.9904i	1.35457	−	0.782064i	0.988886	+	0.148674i	$0.0475004\pi$
$942$		0			0
$943$	−0.821665	+	1.42317i	−0.0267571	+	0.0463447i
$944$	−34.1875	−	21.4734i	−1.11271	−	0.698900i
$945$		0			0
$946$	3.24008	+	12.5586i	0.105344	+	0.408314i
$947$	5.24961	+	3.03086i	0.170589	+	0.0984898i	0.582864	−	0.812570i	$-0.301932\pi$
$947$	5.24961	+	3.03086i	0.170589	+	0.0984898i	−0.412274	+	0.911060i	$0.635265\pi$
$948$		0			0
$949$	−3.17736	+	1.83445i	−0.103141	+	0.0595487i
$950$	4.38738	−	15.7847i	0.142345	−	0.512125i
$951$		0			0
$952$	35.8840	−	31.3250i	1.16301	−	1.01525i
$953$	19.4315			0.629449			0.314725	−	0.949183i	$-0.398088\pi$
$953$	19.4315			0.629449			0.314725	+	0.949183i	$0.398088\pi$
$954$		0			0
$955$	−4.66683	+	2.69439i	−0.151015	+	0.0871885i
$956$	−25.6341	−	15.4431i	−0.829066	−	0.499466i
$957$		0			0
$958$	−10.1688	−	39.4145i	−0.328540	−	1.27342i
$959$	0.720208	−	18.0835i	0.0232567	−	0.583946i
$960$		0			0
$961$	6.30930	−	10.9280i	0.203526	−	0.352517i
$962$	−8.39129	+	8.23651i	−0.270546	+	0.265556i
$963$		0			0
$964$	0.423331	−	22.7375i	0.0136346	−	0.732327i
$965$		−	4.15871i		−	0.133874i
$966$		0			0
$967$	29.3398			0.943505			0.471752	−	0.881731i	$-0.343622\pi$
$967$	29.3398			0.943505			0.471752	+	0.881731i	$0.343622\pi$
$968$	22.5821	−	5.37985i	0.725817	−	0.172915i
$969$		0			0
$970$	0.320587	+	0.326612i	0.0102934	+	0.0104869i
$971$	8.74983	+	5.05171i	0.280795	+	0.162117i	0.633783	−	0.773511i	$-0.281501\pi$
$971$	8.74983	+	5.05171i	0.280795	+	0.162117i	−0.352988	+	0.935628i	$0.614834\pi$
$972$		0			0
$973$	10.8179	−	17.1250i	0.346807	−	0.549003i
$974$	−2.20862	−	8.56063i	−0.0707688	−	0.274300i
$975$		0			0
$976$	−2.27011	+	60.9436i	−0.0726643	+	1.95076i
$977$	23.2401	+	40.2531i	0.743517	+	1.28781i	0.950884	+	0.309546i	$0.100177\pi$
$977$	23.2401	+	40.2531i	0.743517	+	1.28781i	−0.207367	+	0.978263i	$0.566489\pi$
$978$		0			0
$979$		−	11.3760i		−	0.363578i
$980$	−5.52253	+	7.70583i	−0.176411	+	0.246154i
$981$		0			0
$982$	−2.05081	+	7.37831i	−0.0654439	+	0.235451i
$983$	16.9571	+	29.3706i	0.540848	+	0.936777i	0.998856	+	0.0478283i	$0.0152300\pi$
$983$	16.9571	+	29.3706i	0.540848	+	0.936777i	−0.458007	+	0.888948i	$0.651437\pi$
$984$		0			0
$985$	5.13408	−	8.89248i	0.163585	−	0.283338i
$986$	54.6944	−	14.1110i	1.74182	−	0.449386i
$987$		0			0
$988$	−5.71734	+	3.16049i	−0.181893	+	0.100549i
$989$	1.21443	+	0.701150i	0.0386165	+	0.0222953i
$990$		0			0
$991$	−9.87808	−	17.1093i	−0.313787	−	0.543496i	0.665392	−	0.746494i	$-0.268265\pi$
$991$	−9.87808	−	17.1093i	−0.313787	−	0.543496i	−0.979179	+	0.202999i	$0.934931\pi$
$992$	17.9287	−	16.3330i	0.569236	−	0.518573i
$993$		0			0
$994$	−13.7868	−	15.2122i	−0.437292	−	0.482503i
$995$			9.51584i			0.301672i
$996$		0			0
$997$	17.7164	−	10.2285i	0.561083	−	0.323941i	−0.192497	−	0.981298i	$-0.561659\pi$
$997$	17.7164	−	10.2285i	0.561083	−	0.323941i	0.753580	+	0.657356i	$0.228325\pi$
$998$	9.06416	+	9.23448i	0.286921	+	0.292312i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.1		32
3.2	odd	2		168.2.bc.a.37.16	yes	32
4.3	odd	2		2016.2.cr.e.1297.10		32
7.4	even	3	inner	504.2.cj.e.109.13		32
8.3	odd	2		2016.2.cr.e.1297.7		32
8.5	even	2	inner	504.2.cj.e.37.13		32
12.11	even	2		672.2.bk.a.625.12		32
21.2	odd	6		1176.2.c.e.589.7		16
21.5	even	6		1176.2.c.f.589.7		16
21.11	odd	6		168.2.bc.a.109.4	yes	32
24.5	odd	2		168.2.bc.a.37.4	✓	32
24.11	even	2		672.2.bk.a.625.5		32
28.11	odd	6		2016.2.cr.e.1873.7		32
56.11	odd	6		2016.2.cr.e.1873.10		32
56.53	even	6	inner	504.2.cj.e.109.1		32
84.11	even	6		672.2.bk.a.529.5		32
84.23	even	6		4704.2.c.e.2353.13		16
84.47	odd	6		4704.2.c.f.2353.4		16
168.5	even	6		1176.2.c.f.589.8		16
168.11	even	6		672.2.bk.a.529.12		32
168.53	odd	6		168.2.bc.a.109.16	yes	32
168.107	even	6		4704.2.c.e.2353.4		16
168.131	odd	6		4704.2.c.f.2353.13		16
168.149	odd	6		1176.2.c.e.589.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.4	✓	32	24.5	odd	2
168.2.bc.a.37.16	yes	32	3.2	odd	2
168.2.bc.a.109.4	yes	32	21.11	odd	6
168.2.bc.a.109.16	yes	32	168.53	odd	6
504.2.cj.e.37.1		32	1.1	even	1	trivial
504.2.cj.e.37.13		32	8.5	even	2	inner
504.2.cj.e.109.1		32	56.53	even	6	inner
504.2.cj.e.109.13		32	7.4	even	3	inner
672.2.bk.a.529.5		32	84.11	even	6
672.2.bk.a.529.12		32	168.11	even	6
672.2.bk.a.625.5		32	24.11	even	2
672.2.bk.a.625.12		32	12.11	even	2
1176.2.c.e.589.7		16	21.2	odd	6
1176.2.c.e.589.8		16	168.149	odd	6
1176.2.c.f.589.7		16	21.5	even	6
1176.2.c.f.589.8		16	168.5	even	6
2016.2.cr.e.1297.7		32	8.3	odd	2
2016.2.cr.e.1297.10		32	4.3	odd	2
2016.2.cr.e.1873.7		32	28.11	odd	6
2016.2.cr.e.1873.10		32	56.11	odd	6
4704.2.c.e.2353.4		16	168.107	even	6
4704.2.c.e.2353.13		16	84.23	even	6
4704.2.c.f.2353.4		16	84.47	odd	6
4704.2.c.f.2353.13		16	168.131	odd	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.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36256 - 0.378724i) q^{2} +(1.71314 + 1.03207i) q^{4} +(0.586448 + 0.338586i) q^{5} +(2.23683 + 1.41301i) q^{7} +(-1.94338 - 2.05506i) q^{8} +O(q^{10})\)	\(q+(-1.36256 - 0.378724i) q^{2} +(1.71314 + 1.03207i) q^{4} +(0.586448 + 0.338586i) q^{5} +(2.23683 + 1.41301i) q^{7} +(-1.94338 - 2.05506i) q^{8} +(-0.670840 - 0.683446i) q^{10} +(1.44721 - 0.835550i) q^{11} -1.28049i q^{13} +(-2.51267 - 2.77245i) q^{14} +(1.86967 + 3.53615i) q^{16} +(3.18262 + 5.51246i) q^{17} +(-2.20912 - 1.27544i) q^{19} +(0.655221 + 1.18530i) q^{20} +(-2.28836 + 0.590391i) q^{22} +(-0.127760 + 0.221287i) q^{23} +(-2.27072 - 3.93300i) q^{25} +(-0.484953 + 1.74474i) q^{26} +(2.37367 + 4.72924i) q^{28} +6.27489i q^{29} +(2.14368 + 3.71296i) q^{31} +(-1.20831 - 5.52630i) q^{32} +(-2.24881 - 8.71639i) q^{34} +(0.833358 + 1.58602i) q^{35} +(5.62313 + 3.24651i) q^{37} +(2.52702 + 2.57451i) q^{38} +(-0.443876 - 1.86319i) q^{40} +6.43132 q^{41} -5.48802i q^{43} +(3.34162 + 0.0622148i) q^{44} +(0.257887 - 0.253131i) q^{46} +(4.73403 - 8.19958i) q^{47} +(3.00680 + 6.32132i) q^{49} +(1.60447 + 6.21892i) q^{50} +(1.32155 - 2.19365i) q^{52} +(4.91784 - 2.83932i) q^{53} +1.13162 q^{55} +(-1.44318 - 7.34283i) q^{56} +(2.37645 - 8.54991i) q^{58} +(-8.74078 + 5.04649i) q^{59} +(13.2038 + 7.62324i) q^{61} +(-1.51470 - 5.87099i) q^{62} +(-0.446552 + 7.98753i) q^{64} +(0.433556 - 0.750941i) q^{65} +(-13.6595 + 7.88629i) q^{67} +(-0.236977 + 12.7283i) q^{68} +(-0.534837 - 2.47665i) q^{70} +5.48693 q^{71} +(-1.43261 - 2.48136i) q^{73} +(-6.43231 - 6.55318i) q^{74} +(-2.46819 - 4.46496i) q^{76} +(4.41781 + 0.175948i) q^{77} +(6.09527 - 10.5573i) q^{79} +(-0.100827 + 2.70681i) q^{80} +(-8.76305 - 2.43570i) q^{82} -7.63129i q^{83} +4.31036i q^{85} +(-2.07845 + 7.47776i) q^{86} +(-4.52959 - 1.35032i) q^{88} +(3.40374 - 5.89546i) q^{89} +(1.80935 - 2.86424i) q^{91} +(-0.447253 + 0.247237i) q^{92} +(-9.55577 + 9.37952i) q^{94} +(-0.863690 - 1.49595i) q^{95} -0.477890 q^{97} +(-1.70291 - 9.75193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 6 q^{10} - 22 q^{14} - 10 q^{16} + 40 q^{20} - 12 q^{22} + 8 q^{23} + 16 q^{25} - 6 q^{26} - 26 q^{28} - 24 q^{31} + 8 q^{32} - 24 q^{34} + 26 q^{38} - 6 q^{40} - 20 q^{44} + 16 q^{46} + 24 q^{47} + 8 q^{49} - 52 q^{50} + 44 q^{52} - 64 q^{55} - 40 q^{56} + 34 q^{58} - 100 q^{62} - 20 q^{64} - 16 q^{68} + 38 q^{70} + 80 q^{71} + 8 q^{73} - 10 q^{74} - 32 q^{76} + 8 q^{79} + 56 q^{80} + 22 q^{86} + 50 q^{88} - 64 q^{92} - 48 q^{94} - 24 q^{95} - 48 q^{97} + 64 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 6 * q^10 - 22 * q^14 - 10 * q^16 + 40 * q^20 - 12 * q^22 + 8 * q^23 + 16 * q^25 - 6 * q^26 - 26 * q^28 - 24 * q^31 + 8 * q^32 - 24 * q^34 + 26 * q^38 - 6 * q^40 - 20 * q^44 + 16 * q^46 + 24 * q^47 + 8 * q^49 - 52 * q^50 + 44 * q^52 - 64 * q^55 - 40 * q^56 + 34 * q^58 - 100 * q^62 - 20 * q^64 - 16 * q^68 + 38 * q^70 + 80 * q^71 + 8 * q^73 - 10 * q^74 - 32 * q^76 + 8 * q^79 + 56 * q^80 + 22 * q^86 + 50 * q^88 - 64 * q^92 - 48 * q^94 - 24 * q^95 - 48 * q^97 + 64 * q^98

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