LMFDB - Embedded newform 504.2.cj.e.109.1

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			109.1
Character	$\chi$	$=$	504.109
Dual form			504.2.cj.e.37.1

$q$-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 $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

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	−0.363101	−	0.931750i	$-0.618282\pi$
$5$	0.586448	−	0.338586i	0.262268	−	0.151420i	0.625369	+	0.780330i	$0.284949\pi$
$6$		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	0.702049	−	0.712129i	$-0.252269\pi$
$11$	1.44721	+	0.835550i	0.436352	+	0.251928i	−0.265697	+	0.964057i	$0.585602\pi$
$12$		0			0
$13$			1.28049i			0.355144i	0.984108	+	0.177572i	$0.0568243\pi$
$13$			1.28049i			0.355144i	−0.984108	+	0.177572i	$0.943176\pi$
$14$	−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	−0.164622	−	0.986357i	$-0.552640\pi$
$17$	3.18262	−	5.51246i	0.771899	−	1.33697i	0.936521	−	0.350611i	$-0.114026\pi$
$18$		0			0
$19$	−2.20912	+	1.27544i	−0.506807	+	0.292605i	−0.731520	−	0.681820i	$-0.761189\pi$
$19$	−2.20912	+	1.27544i	−0.506807	+	0.292605i	0.224713	+	0.974425i	$0.427856\pi$
$20$	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	0.852398	−	0.522893i	$-0.175147\pi$
$23$	−0.127760	−	0.221287i	−0.0266398	−	0.0461415i	−0.879038	+	0.476752i	$0.841814\pi$
$24$		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	$-0.802032\pi$
$29$		−	6.27489i		−	1.16522i	0.812753	−	0.582609i	$-0.197968\pi$
$30$		0			0
$31$	2.14368	−	3.71296i	0.385016	−	0.666867i	−0.606756	−	0.794888i	$-0.707529\pi$
$31$	2.14368	−	3.71296i	0.385016	−	0.666867i	0.991771	+	0.128022i	$0.0408627\pi$
$32$	−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	0.0393887	−	0.999224i	$-0.487459\pi$
$37$	5.62313	−	3.24651i	0.924436	−	0.533724i	0.885048	+	0.465500i	$0.154126\pi$
$38$	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	$0.137429\pi$
$43$			5.48802i			0.836916i	−0.908236	+	0.418458i	$0.862571\pi$
$44$	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	0.971665	+	0.236363i	$0.0759556\pi$
$47$	4.73403	+	8.19958i	0.690529	+	1.19603i	−0.281136	+	0.959668i	$0.590711\pi$
$48$		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	0.798164	−	0.602440i	$-0.205805\pi$
$53$	4.91784	+	2.83932i	0.675518	+	0.390010i	−0.122647	+	0.992450i	$0.539138\pi$
$54$		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	−0.192030	−	0.981389i	$-0.561507\pi$
$59$	−8.74078	−	5.04649i	−1.13795	−	0.656997i	−0.945923	+	0.324392i	$0.894840\pi$
$60$		0			0
$61$	13.2038	−	7.62324i	1.69058	−	0.976056i	0.736529	−	0.676406i	$-0.236464\pi$
$61$	13.2038	−	7.62324i	1.69058	−	0.976056i	0.954049	−	0.299650i	$-0.0968698\pi$
$62$	−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	−0.968304	−	0.249776i	$-0.919643\pi$
$67$	−13.6595	−	7.88629i	−1.66877	−	0.963464i	−0.700465	−	0.713687i	$-0.747024\pi$
$68$	−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	−0.937602	−	0.347711i	$-0.886959\pi$
$73$	−1.43261	+	2.48136i	−0.167675	+	0.290421i	0.769927	+	0.638132i	$0.220293\pi$
$74$	−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	0.973194	+	0.229986i	$0.0738682\pi$
$79$	6.09527	+	10.5573i	0.685771	+	1.18779i	−0.287423	+	0.957804i	$0.592798\pi$
$80$	−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	$0.137557\pi$
$83$			7.63129i			0.837643i	−0.908069	+	0.418822i	$0.862443\pi$
$84$		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	0.988092	−	0.153864i	$-0.0491717\pi$
$89$	3.40374	+	5.89546i	0.360796	+	0.624917i	−0.627296	+	0.778781i	$0.715838\pi$
$90$		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	−0.190520	−	0.981683i	$-0.561018\pi$
$101$	−11.4161	−	6.59108i	−1.13594	−	0.655837i	−0.945423	+	0.325846i	$0.894351\pi$
$102$		0			0
$103$	−0.808712	−	1.40073i	−0.0796848	−	0.138018i	0.823429	−	0.567419i	$-0.192058\pi$
$103$	−0.808712	−	1.40073i	−0.0796848	−	0.138018i	−0.903114	+	0.429401i	$0.858725\pi$
$104$	−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	−0.887754	−	0.460319i	$-0.847735\pi$
$107$	−9.65085	+	5.57192i	−0.932983	+	0.538658i	−0.0452293	+	0.998977i	$0.514402\pi$
$108$		0			0
$109$	−3.49609	−	2.01847i	−0.334865	−	0.193334i	0.323134	−	0.946353i	$-0.395264\pi$
$109$	−3.49609	−	2.01847i	−0.334865	−	0.193334i	−0.657999	+	0.753019i	$0.728597\pi$
$110$	−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	−0.411466	−	0.911425i	$-0.634983\pi$
$131$	1.96999	−	1.13738i	0.172119	−	0.0993730i	0.583585	+	0.812052i	$0.301650\pi$
$132$		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	−0.974331	−	0.225122i	$-0.927722\pi$
$137$	−3.42016	+	5.92390i	−0.292204	+	0.506113i	0.682126	+	0.731234i	$0.261055\pi$
$138$		0			0
$139$			7.65594i			0.649369i	0.945822	+	0.324684i	$0.105258\pi$
$139$			7.65594i			0.649369i	−0.945822	+	0.324684i	$0.894742\pi$
$140$	−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	0.0601715	−	0.998188i	$-0.480835\pi$
$149$	11.6538	−	6.72830i	0.954714	−	0.551204i	0.894542	+	0.446984i	$0.147502\pi$
$150$		0			0
$151$	−7.92722	+	13.7303i	−0.645108	+	1.11736i	0.339169	+	0.940726i	$0.389854\pi$
$151$	−7.92722	+	13.7303i	−0.645108	+	1.11736i	−0.984277	+	0.176634i	$0.943479\pi$
$152$	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	0.0183949	−	0.999831i	$-0.494144\pi$
$157$	−10.5037	−	6.06431i	−0.838286	−	0.483985i	−0.856681	+	0.515846i	$0.827478\pi$
$158$	−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	−0.992843	−	0.119430i	$-0.961893\pi$
$163$	−17.6931	+	10.2151i	−1.38583	+	0.800112i	−0.392992	+	0.919542i	$0.628560\pi$
$164$	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	−0.350380	−	0.936608i	$-0.613948\pi$
$173$	3.75589	−	2.16847i	0.285555	−	0.164865i	0.635936	+	0.771742i	$0.280614\pi$
$174$		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	0.690193	−	0.723625i	$-0.257525\pi$
$179$	5.46686	+	3.15629i	0.408612	+	0.235912i	−0.281581	+	0.959537i	$0.590859\pi$
$180$		0			0
$181$			12.0671i			0.896938i	0.893798	+	0.448469i	$0.148031\pi$
$181$			12.0671i			0.896938i	−0.893798	+	0.448469i	$0.851969\pi$
$182$	−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	0.685406	−	0.728161i	$-0.259625\pi$
$191$	−3.97889	−	6.89164i	−0.287902	−	0.498662i	−0.973309	+	0.229499i	$0.926291\pi$
$192$		0			0
$193$	−3.07064	+	5.31851i	−0.221030	+	0.382835i	−0.955121	−	0.296216i	$-0.904275\pi$
$193$	−3.07064	+	5.31851i	−0.221030	+	0.382835i	0.734091	+	0.679051i	$0.237608\pi$
$194$	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	$0.181640\pi$
$197$			15.1633i			1.08034i	−0.841556	+	0.540170i	$0.818360\pi$
$198$		0			0
$199$	7.02616	−	12.1697i	0.498071	−	0.862685i	−0.501926	−	0.864910i	$-0.667375\pi$
$199$	7.02616	−	12.1697i	0.498071	−	0.862685i	0.999998	+	0.00222556i	$0.000708420\pi$
$200$	−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	$0.115166\pi$
$211$			10.2832i			0.707926i	−0.935259	+	0.353963i	$0.884834\pi$
$212$	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	0.995682	+	0.0928278i	$0.0295906\pi$
$227$	23.7134	+	13.6909i	1.57391	+	0.908700i	0.578232	+	0.815872i	$0.303743\pi$
$228$		0			0
$229$	10.2388	−	5.91138i	0.676599	−	0.390635i	−0.121973	−	0.992533i	$-0.538922\pi$
$229$	10.2388	−	5.91138i	0.676599	−	0.390635i	0.798573	+	0.601899i	$0.205589\pi$
$230$	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	0.979614	−	0.200889i	$-0.0643829\pi$
$233$	4.82097	+	8.35017i	0.315833	+	0.547038i	−0.663782	+	0.747926i	$0.731050\pi$
$234$		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	−0.988972	−	0.148101i	$-0.952684\pi$
$241$	−5.68537	+	9.84735i	−0.366227	+	0.634324i	0.622745	+	0.782425i	$0.286017\pi$
$242$	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	$0.0378309\pi$
$251$			3.75699i			0.237139i	−0.992946	+	0.118570i	$0.962169\pi$
$252$		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	0.667023	−	0.745037i	$-0.267568\pi$
$257$	−4.99709	−	8.65522i	−0.311710	−	0.539898i	−0.978733	+	0.205140i	$0.934235\pi$
$258$		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	−0.999249	−	0.0387438i	$-0.987664\pi$
$263$	−7.55841	+	13.0915i	−0.466071	+	0.807259i	0.533178	+	0.846003i	$0.320998\pi$
$264$		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	0.229586	−	0.973288i	$-0.426263\pi$
$269$	−8.17624	−	4.72055i	−0.498514	−	0.287817i	−0.728100	+	0.685471i	$0.759596\pi$
$270$		0			0
$271$	−8.43032	−	14.6017i	−0.512106	−	0.886993i	−0.999902	−	0.0140351i	$-0.995532\pi$
$271$	−8.43032	−	14.6017i	−0.512106	−	0.886993i	0.487796	−	0.872958i	$-0.337801\pi$
$272$	−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	0.715156	−	0.698965i	$-0.246356\pi$
$277$	7.77929	+	4.49138i	0.467412	+	0.269861i	−0.247744	+	0.968826i	$0.579689\pi$
$278$	−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	0.895031	−	0.446004i	$-0.147153\pi$
$283$	16.0874	+	9.28805i	0.956296	+	0.552118i	0.0612647	+	0.998122i	$0.480487\pi$
$284$	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	$0.150208\pi$
$293$			15.5621i			0.909145i	−0.890710	+	0.454573i	$0.849792\pi$
$294$		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	$-0.692457\pi$
$307$		−	28.8304i		−	1.64544i	0.568450	−	0.822718i	$-0.307543\pi$
$308$	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	−0.984837	−	0.173484i	$-0.944498\pi$
$311$	−6.03436	+	10.4518i	−0.342177	+	0.592668i	0.642660	+	0.766152i	$0.277831\pi$
$312$		0			0
$313$	14.5841	+	25.2604i	0.824343	+	1.42780i	0.902421	+	0.430856i	$0.141788\pi$
$313$	14.5841	+	25.2604i	0.824343	+	1.42780i	−0.0780780	+	0.996947i	$0.524878\pi$
$314$	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	−0.861135	−	0.508377i	$-0.830246\pi$
$317$	−15.1594	+	8.75226i	−0.851435	+	0.491576i	0.00969989	+	0.999953i	$0.496912\pi$
$318$		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	−0.527525	−	0.849540i	$-0.676880\pi$
$331$	−1.01090	+	0.583642i	−0.0555640	+	0.0320799i	0.471961	+	0.881620i	$0.343546\pi$
$332$	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	−0.0553515	−	0.998467i	$-0.517628\pi$
$347$	−17.6542	−	10.1926i	−0.947725	−	0.547169i	−0.892373	+	0.451298i	$0.850961\pi$
$348$		0			0
$349$			16.5765i			0.887321i	0.896195	+	0.443661i	$0.146320\pi$
$349$			16.5765i			0.887321i	−0.896195	+	0.443661i	$0.853680\pi$
$350$	−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	−0.274063	−	0.961712i	$-0.588368\pi$
$353$	13.0736	−	22.6441i	0.695835	−	1.20522i	0.969898	−	0.243510i	$-0.0782988\pi$
$354$		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	0.858345	−	0.513073i	$-0.171493\pi$
$359$	−0.287276	−	0.497577i	−0.0151619	−	0.0262611i	−0.873507	+	0.486812i	$0.838160\pi$
$360$		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	−0.490696	−	0.871331i	$-0.663257\pi$
$367$	9.75576	−	16.8975i	0.509247	−	0.882041i	0.999943	−	0.0107103i	$-0.00340926\pi$
$368$	−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	−0.872153	−	0.489233i	$-0.837277\pi$
$373$	−17.0833	+	9.86307i	−0.884542	+	0.510691i	−0.0123886	+	0.999923i	$0.503944\pi$
$374$	−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	$0.0877395\pi$
$379$			10.5970i			0.544329i	−0.962251	+	0.272165i	$0.912260\pi$
$380$	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	0.999947	−	0.0103232i	$-0.00328603\pi$
$383$	9.60971	+	16.6445i	0.491033	+	0.850494i	−0.508913	+	0.860818i	$0.669953\pi$
$384$		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	−0.178453	−	0.983948i	$-0.557109\pi$
$389$	−22.0860	−	12.7513i	−1.11980	−	0.646519i	−0.941351	+	0.337429i	$0.890443\pi$
$390$		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	−0.993536	−	0.113514i	$-0.963789\pi$
$397$	−27.7354	+	16.0130i	−1.39200	+	0.803671i	−0.398462	+	0.917185i	$0.630456\pi$
$398$	−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	−0.993198	−	0.116438i	$-0.962852\pi$
$401$	−11.9637	−	20.7217i	−0.597437	−	1.03479i	0.395761	−	0.918354i	$-0.370481\pi$
$402$		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	−0.980343	−	0.197303i	$-0.936782\pi$
$409$	−6.45748	+	11.1847i	−0.319302	+	0.553047i	0.661041	+	0.750350i	$0.270115\pi$
$410$	−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	$-0.711275\pi$
$419$		−	32.2474i		−	1.57539i	0.616066	−	0.787694i	$-0.288725\pi$
$420$		0			0
$421$		−	28.8215i		−	1.40468i	−0.711844	−	0.702338i	$-0.752140\pi$
$421$		−	28.8215i		−	1.40468i	0.711844	−	0.702338i	$-0.247860\pi$
$422$	−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	−0.941975	−	0.335683i	$-0.891033\pi$
$431$	−3.74266	+	6.48247i	−0.180277	+	0.312250i	0.761698	+	0.647933i	$0.224366\pi$
$432$		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	0.900872	+	0.434086i	$0.142928\pi$
$439$	17.3143	+	29.9892i	0.826365	+	1.43131i	−0.0745068	+	0.997221i	$0.523738\pi$
$440$	−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	−0.364895	−	0.931049i	$-0.618895\pi$
$443$	5.45067	−	3.14695i	0.258969	−	0.149516i	0.623864	+	0.781533i	$0.285562\pi$
$444$		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	0.995138	+	0.0984951i	$0.0314029\pi$
$457$	12.4603	+	21.5819i	0.582868	+	1.00956i	−0.412270	+	0.911062i	$0.635264\pi$
$458$	−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	$-0.962488\pi$
$461$		−	5.04894i		−	0.235153i	0.993064	−	0.117576i	$-0.0375125\pi$
$462$		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	0.275990	−	0.961160i	$-0.410994\pi$
$467$	26.9344	−	15.5506i	1.24637	−	0.719595i	0.970384	+	0.241566i	$0.0776610\pi$
$468$		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	−0.323684	−	0.946165i	$-0.604921\pi$
$479$	14.3914	−	24.9267i	0.657561	−	1.13893i	0.981245	−	0.192764i	$-0.0617453\pi$
$480$		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	−0.786474	−	0.617624i	$-0.788095\pi$
$487$	3.12575	−	5.41395i	0.141641	−	0.245330i	0.928115	+	0.372294i	$0.121429\pi$
$488$	−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	$0.0389913\pi$
$491$			5.41504i			0.244377i	−0.992507	+	0.122189i	$0.961009\pi$
$492$		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	−0.666763	−	0.745270i	$-0.732321\pi$
$499$	−7.92389	+	4.57486i	−0.354722	+	0.204799i	0.312041	+	0.950069i	$0.398987\pi$
$500$	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	0.284838	−	0.958576i	$-0.408060\pi$
$509$	28.3684	−	16.3785i	1.25741	−	0.725965i	0.972570	+	0.232610i	$0.0747267\pi$
$510$		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	−0.998376	−	0.0569688i	$-0.981856\pi$
$521$	−10.2681	+	17.7848i	−0.449852	+	0.779166i	0.548524	+	0.836135i	$0.315190\pi$
$522$		0			0
$523$	−11.2213	+	6.47863i	−0.490674	+	0.283291i	−0.724854	−	0.688902i	$-0.758093\pi$
$523$	−11.2213	+	6.47863i	−0.490674	+	0.283291i	0.234180	+	0.972193i	$0.424760\pi$
$524$	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	0.199324	−	0.979934i	$-0.436125\pi$
$541$	26.6933	−	15.4114i	1.14763	−	0.662586i	0.948309	+	0.317347i	$0.102792\pi$
$542$	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	$-0.912392\pi$
$547$		−	12.7122i		−	0.543537i	0.962363	−	0.271768i	$-0.0876084\pi$
$548$	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	0.679164	−	0.733987i	$-0.262343\pi$
$557$	9.04134	+	5.22002i	0.383094	+	0.221179i	−0.296070	+	0.955166i	$0.595676\pi$
$558$		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	0.231083	−	0.972934i	$-0.425773\pi$
$563$	−11.7680	−	6.79424i	−0.495961	−	0.286343i	−0.727044	+	0.686591i	$0.759106\pi$
$564$		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	0.987706	−	0.156321i	$-0.0499633\pi$
$569$	8.55098	+	14.8107i	0.358476	+	0.620898i	−0.629231	+	0.777219i	$0.716630\pi$
$570$		0			0
$571$	−0.502264	−	0.289982i	−0.0210191	−	0.0121354i	0.489454	−	0.872029i	$-0.337196\pi$
$571$	−0.502264	−	0.289982i	−0.0210191	−	0.0121354i	−0.510473	+	0.859894i	$0.670530\pi$
$572$	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	−0.636382	−	0.771374i	$-0.719570\pi$
$577$	8.40341	−	14.5551i	0.349838	−	0.605938i	0.986221	+	0.165436i	$0.0529031\pi$
$578$	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	$-0.824680\pi$
$587$		−	25.3598i		−	1.04671i	0.852114	−	0.523356i	$-0.175320\pi$
$588$		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	0.744312	−	0.667832i	$-0.232777\pi$
$593$	−5.02137	−	8.69726i	−0.206203	−	0.357154i	−0.950515	+	0.310678i	$0.899444\pi$
$594$		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	−0.828915	−	0.559374i	$-0.811041\pi$
$599$	1.71260	−	2.96631i	0.0699750	−	0.121200i	0.898890	+	0.438174i	$0.144375\pi$
$600$		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	0.914619	−	0.404316i	$-0.132491\pi$
$607$	2.64017	+	4.57291i	0.107161	+	0.185609i	−0.807458	+	0.589925i	$0.799157\pi$
$608$	−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	0.936149	−	0.351602i	$-0.114363\pi$
$613$	27.2280	+	15.7201i	1.09973	+	0.634928i	0.163578	+	0.986530i	$0.447696\pi$
$614$	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	0.945771	−	0.324835i	$-0.105309\pi$
$619$	28.2967	+	16.3371i	1.13734	+	0.656644i	0.191570	+	0.981479i	$0.438642\pi$
$620$	−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	−0.996659	−	0.0816797i	$-0.973972\pi$
$641$	−10.8258	+	18.7508i	−0.427593	+	0.740612i	0.569066	+	0.822292i	$0.307305\pi$
$642$		0			0
$643$		−	5.48021i		−	0.216118i	−0.994144	−	0.108059i	$-0.965536\pi$
$643$		−	5.48021i		−	0.216118i	0.994144	−	0.108059i	$-0.0344636\pi$
$644$	−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	−0.380672	−	0.924710i	$-0.624307\pi$
$647$	15.5285	−	26.8961i	0.610487	−	1.05739i	0.991158	−	0.132684i	$-0.0423594\pi$
$648$		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	−0.277191	−	0.960815i	$-0.589404\pi$
$653$	10.6381	−	6.14194i	0.416303	−	0.240353i	0.693494	+	0.720462i	$0.256070\pi$
$654$		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	$0.0804091\pi$
$659$			12.8321i			0.499869i	−0.968263	+	0.249934i	$0.919591\pi$
$660$		0			0
$661$	−11.1865	−	6.45853i	−0.435104	−	0.251208i	0.266415	−	0.963859i	$-0.414161\pi$
$661$	−11.1865	−	6.45853i	−0.435104	−	0.251208i	−0.701519	+	0.712651i	$0.747494\pi$
$662$	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	−0.993784	−	0.111326i	$-0.964490\pi$
$677$	−36.2777	+	20.9449i	−1.39427	+	0.804979i	−0.400481	+	0.916305i	$0.631157\pi$
$678$		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	0.557789	−	0.829983i	$-0.311650\pi$
$683$	3.08116	+	1.77891i	0.117897	+	0.0680680i	−0.439892	+	0.898051i	$0.644983\pi$
$684$		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	−0.559065	−	0.829124i	$-0.688840\pi$
$691$	−3.16904	+	1.82965i	−0.120556	+	0.0696031i	0.438509	+	0.898727i	$0.355507\pi$
$692$	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	$-0.921844\pi$
$701$		−	12.8715i		−	0.486151i	0.970007	−	0.243076i	$-0.0781563\pi$
$702$		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	0.353606	−	0.935395i	$-0.384955\pi$
$709$	35.6931	−	20.6074i	1.34048	−	0.773929i	0.986878	+	0.161466i	$0.0516221\pi$
$710$	−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	−0.999207	−	0.0398069i	$-0.987326\pi$
$719$	−14.3208	−	24.8044i	−0.534078	−	0.925049i	0.465130	−	0.885242i	$-0.346008\pi$
$720$		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	−0.352917	−	0.935655i	$-0.614810\pi$
$733$	7.60577	−	4.39119i	0.280926	−	0.162192i	0.633842	+	0.773462i	$0.281477\pi$
$734$	−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	0.842808	−	0.538214i	$-0.180901\pi$
$739$	21.6962	+	12.5263i	0.798106	+	0.460787i	−0.0447026	+	0.999000i	$0.514234\pi$
$740$	−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	−0.994155	−	0.107959i	$-0.965569\pi$
$751$	−16.1843	−	28.0320i	−0.590573	−	1.02290i	0.403583	−	0.914943i	$-0.367765\pi$
$752$	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	$0.0297716\pi$
$757$			5.13921i			0.186788i	−0.995629	+	0.0933940i	$0.970228\pi$
$758$	−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	0.977712	−	0.209949i	$-0.0673299\pi$
$761$	8.46993	+	14.6704i	0.307035	+	0.531800i	−0.670677	+	0.741749i	$0.733997\pi$
$762$		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	−0.380936	−	0.924601i	$-0.624398\pi$
$773$	−38.1492	−	22.0255i	−1.37213	−	0.792201i	−0.991196	+	0.132400i	$0.957732\pi$
$774$		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	0.835082	−	0.550125i	$-0.185420\pi$
$787$	21.7752	+	12.5719i	0.776202	+	0.448140i	−0.0588808	+	0.998265i	$0.518753\pi$
$788$	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	$0.429314\pi$
$797$			55.0759i			1.95089i	−0.220247	+	0.975444i	$0.570686\pi$
$798$		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	−0.879434	−	0.476022i	$-0.842078\pi$
$809$	−0.781329	+	1.35330i	−0.0274701	+	0.0475796i	0.851964	+	0.523601i	$0.175412\pi$
$810$		0			0
$811$		−	24.5686i		−	0.862720i	−0.902180	−	0.431360i	$-0.858034\pi$
$811$		−	24.5686i		−	0.862720i	0.902180	−	0.431360i	$-0.141966\pi$
$812$	−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	0.581495	−	0.813550i	$-0.302468\pi$
$821$	45.1801	−	26.0848i	1.57680	−	0.910365i	0.995302	−	0.0968147i	$-0.0308654\pi$
$822$		0			0
$823$	9.19076	−	15.9189i	0.320370	−	0.554897i	−0.660195	−	0.751095i	$-0.729526\pi$
$823$	9.19076	−	15.9189i	0.320370	−	0.554897i	0.980564	+	0.196198i	$0.0628595\pi$
$824$	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	$0.0556275\pi$
$827$			10.0002i			0.347742i	−0.984768	+	0.173871i	$0.944372\pi$
$828$		0			0
$829$	−33.3708	−	19.2666i	−1.15902	−	0.669158i	−0.207948	−	0.978140i	$-0.566679\pi$
$829$	−33.3708	−	19.2666i	−1.15902	−	0.669158i	−0.951068	+	0.308982i	$0.900012\pi$
$830$	−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	$-0.982737\pi$
$853$		−	3.16642i		−	0.108416i	0.998530	−	0.0542080i	$-0.0172634\pi$
$854$	−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	−0.941146	−	0.337999i	$-0.890250\pi$
$857$	−5.20669	+	9.01825i	−0.177857	+	0.308058i	0.763289	+	0.646057i	$0.223583\pi$
$858$		0			0
$859$	−30.4427	+	17.5761i	−1.03869	+	0.599689i	−0.919463	−	0.393178i	$-0.871376\pi$
$859$	−30.4427	+	17.5761i	−1.03869	+	0.599689i	−0.119229	+	0.992867i	$0.538042\pi$
$860$	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	0.998715	+	0.0506844i	$0.0161403\pi$
$863$	15.9590	+	27.6418i	0.543251	+	0.940939i	−0.455463	+	0.890255i	$0.650526\pi$
$864$		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	−0.112636	−	0.993636i	$-0.535930\pi$
$877$	20.4800	−	11.8241i	0.691560	−	0.399272i	0.804196	+	0.594364i	$0.202596\pi$
$878$	−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	$0.185606\pi$
$883$			32.7233i			1.10123i	−0.834760	+	0.550613i	$0.814394\pi$
$884$	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	0.701634	−	0.712537i	$-0.252454\pi$
$887$	−7.92985	−	13.7349i	−0.266258	−	0.461173i	−0.967892	+	0.251365i	$0.919121\pi$
$888$		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	−0.0409010	−	0.999163i	$-0.513023\pi$
$907$	−27.9075	−	16.1124i	−0.926652	−	0.535003i	−0.885751	+	0.464160i	$0.846356\pi$
$908$	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	0.826276	−	0.563266i	$-0.190455\pi$
$919$	−2.26347	−	3.92045i	−0.0746650	−	0.129324i	−0.900941	+	0.433943i	$0.857122\pi$
$920$	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	0.682496	−	0.730889i	$-0.260894\pi$
$929$	−8.89148	−	15.4005i	−0.291720	−	0.505274i	−0.974217	+	0.225615i	$0.927561\pi$
$930$		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	0.988886	−	0.148674i	$-0.0475004\pi$
$941$	41.5525	+	23.9904i	1.35457	+	0.782064i	0.365688	+	0.930738i	$0.380834\pi$
$942$		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	−0.412274	−	0.911060i	$-0.635265\pi$
$947$	5.24961	−	3.03086i	0.170589	−	0.0984898i	0.582864	+	0.812570i	$0.301932\pi$
$948$		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	−0.352988	−	0.935628i	$-0.614834\pi$
$971$	8.74983	−	5.05171i	0.280795	−	0.162117i	0.633783	+	0.773511i	$0.281501\pi$
$972$		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	−0.207367	−	0.978263i	$-0.566489\pi$
$977$	23.2401	−	40.2531i	0.743517	−	1.28781i	0.950884	−	0.309546i	$-0.100177\pi$
$978$		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	−0.458007	−	0.888948i	$-0.651437\pi$
$983$	16.9571	−	29.3706i	0.540848	−	0.936777i	0.998856	−	0.0478283i	$-0.0152300\pi$
$984$		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	−0.979179	−	0.202999i	$-0.934931\pi$
$991$	−9.87808	+	17.1093i	−0.313787	+	0.543496i	0.665392	+	0.746494i	$0.268265\pi$
$992$	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	0.753580	−	0.657356i	$-0.228325\pi$
$997$	17.7164	+	10.2285i	0.561083	+	0.323941i	−0.192497	+	0.981298i	$0.561659\pi$
$998$	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.109.1		32
3.2	odd	2		168.2.bc.a.109.16	yes	32
4.3	odd	2		2016.2.cr.e.1873.10		32
7.2	even	3	inner	504.2.cj.e.37.13		32
8.3	odd	2		2016.2.cr.e.1873.7		32
8.5	even	2	inner	504.2.cj.e.109.13		32
12.11	even	2		672.2.bk.a.529.12		32
21.2	odd	6		168.2.bc.a.37.4	✓	32
21.11	odd	6		1176.2.c.e.589.8		16
21.17	even	6		1176.2.c.f.589.8		16
24.5	odd	2		168.2.bc.a.109.4	yes	32
24.11	even	2		672.2.bk.a.529.5		32
28.23	odd	6		2016.2.cr.e.1297.7		32
56.37	even	6	inner	504.2.cj.e.37.1		32
56.51	odd	6		2016.2.cr.e.1297.10		32
84.11	even	6		4704.2.c.e.2353.4		16
84.23	even	6		672.2.bk.a.625.5		32
84.59	odd	6		4704.2.c.f.2353.13		16
168.11	even	6		4704.2.c.e.2353.13		16
168.53	odd	6		1176.2.c.e.589.7		16
168.59	odd	6		4704.2.c.f.2353.4		16
168.101	even	6		1176.2.c.f.589.7		16
168.107	even	6		672.2.bk.a.625.12		32
168.149	odd	6		168.2.bc.a.37.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.4	✓	32	21.2	odd	6
168.2.bc.a.37.16	yes	32	168.149	odd	6
168.2.bc.a.109.4	yes	32	24.5	odd	2
168.2.bc.a.109.16	yes	32	3.2	odd	2
504.2.cj.e.37.1		32	56.37	even	6	inner
504.2.cj.e.37.13		32	7.2	even	3	inner
504.2.cj.e.109.1		32	1.1	even	1	trivial
504.2.cj.e.109.13		32	8.5	even	2	inner
672.2.bk.a.529.5		32	24.11	even	2
672.2.bk.a.529.12		32	12.11	even	2
672.2.bk.a.625.5		32	84.23	even	6
672.2.bk.a.625.12		32	168.107	even	6
1176.2.c.e.589.7		16	168.53	odd	6
1176.2.c.e.589.8		16	21.11	odd	6
1176.2.c.f.589.7		16	168.101	even	6
1176.2.c.f.589.8		16	21.17	even	6
2016.2.cr.e.1297.7		32	28.23	odd	6
2016.2.cr.e.1297.10		32	56.51	odd	6
2016.2.cr.e.1873.7		32	8.3	odd	2
2016.2.cr.e.1873.10		32	4.3	odd	2
4704.2.c.e.2353.4		16	84.11	even	6
4704.2.c.e.2353.13		16	168.11	even	6
4704.2.c.f.2353.4		16	168.59	odd	6
4704.2.c.f.2353.13		16	84.59	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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