LMFDB - Embedded newform 504.2.cj.e.37.16

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			37.16
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40107 + 0.192386i) q^{2} +(1.92598 + 0.539091i) q^{4} +(2.93503 + 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 + 1.12583i) q^{8} +O(q^{10})$	\(q+(1.40107 + 0.192386i) q^{2} +(1.92598 + 0.539091i) q^{4} +(2.93503 + 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 + 1.12583i) q^{8} +(3.78617 + 2.93882i) q^{10} +(-0.0932820 + 0.0538564i) q^{11} -1.50033i q^{13} +(-2.23193 - 3.00308i) q^{14} +(3.41876 + 2.07655i) q^{16} +(0.214800 + 0.372045i) q^{17} +(-4.32799 - 2.49877i) q^{19} +(4.73929 + 4.84589i) q^{20} +(-0.141056 + 0.0575103i) q^{22} +(-4.56401 + 7.90510i) q^{23} +(3.24294 + 5.61694i) q^{25} +(0.288642 - 2.10206i) q^{26} +(-2.54934 - 4.63690i) q^{28} -7.95437i q^{29} +(-0.393116 - 0.680897i) q^{31} +(4.39041 + 3.56711i) q^{32} +(0.229373 + 0.562584i) q^{34} +(-2.23582 - 8.68345i) q^{35} +(7.68900 + 4.43925i) q^{37} +(-5.58307 - 4.33358i) q^{38} +(5.70777 + 7.70119i) q^{40} -8.59425 q^{41} -6.65201i q^{43} +(-0.208692 + 0.0534386i) q^{44} +(-7.91532 + 10.1975i) q^{46} +(2.87493 - 4.97953i) q^{47} +(-0.137086 + 6.99866i) q^{49} +(3.46295 + 8.49360i) q^{50} +(0.808814 - 2.88960i) q^{52} +(-0.286078 + 0.165167i) q^{53} -0.365048 q^{55} +(-2.67972 - 6.98707i) q^{56} +(1.53031 - 11.1446i) q^{58} +(-8.63850 + 4.98744i) q^{59} +(-1.76996 - 1.02189i) q^{61} +(-0.419787 - 1.02961i) q^{62} +(5.46500 + 5.84241i) q^{64} +(2.54237 - 4.40351i) q^{65} +(2.79312 - 1.61261i) q^{67} +(0.213134 + 0.832346i) q^{68} +(-1.46196 - 12.5962i) q^{70} +8.72656 q^{71} +(-4.38649 - 7.59762i) q^{73} +(9.91876 + 7.69894i) q^{74} +(-6.98854 - 7.14574i) q^{76} +(0.274535 + 0.0764506i) q^{77} +(-0.785733 + 1.36093i) q^{79} +(6.51537 + 11.8880i) q^{80} +(-12.0411 - 1.65341i) q^{82} -1.33259i q^{83} +1.45595i q^{85} +(1.27975 - 9.31991i) q^{86} +(-0.302673 + 0.0347215i) q^{88} +(-3.62404 + 6.27701i) q^{89} +(-2.83421 + 2.77924i) q^{91} +(-13.0517 + 12.7646i) q^{92} +(4.98596 - 6.42355i) q^{94} +(-8.46852 - 14.6679i) q^{95} -19.0450 q^{97} +(-1.53851 + 9.77921i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.40107	+	0.192386i	0.990704	+	0.136037i
$2$	1.40107	+	0.192386i	0.990704	+	0.136037i
$3$		0			0
$3$		0			0
$4$	1.92598	+	0.539091i	0.962988	+	0.269546i
$5$	2.93503	+	1.69454i	1.31259	+	0.757822i	0.982524	−	0.186137i	$-0.0595969\pi$
$5$	2.93503	+	1.69454i	1.31259	+	0.757822i	0.330062	+	0.943959i	$0.392930\pi$
$6$		0			0
$7$	−1.85242	−	1.88906i	−0.700149	−	0.713997i
$7$	−1.85242	−	1.88906i	−0.700149	−	0.713997i
$8$	2.59471	+	1.12583i	0.917367	+	0.398042i
$9$		0			0
$10$	3.78617	+	2.93882i	1.19729	+	0.929338i
$11$	−0.0932820	+	0.0538564i	−0.0281256	+	0.0162383i	−0.513997	−	0.857792i	$-0.671836\pi$
$11$	−0.0932820	+	0.0538564i	−0.0281256	+	0.0162383i	0.485871	+	0.874030i	$0.338502\pi$
$12$		0			0
$13$		−	1.50033i		−	0.416116i	−0.978116	−	0.208058i	$-0.933286\pi$
$13$		−	1.50033i		−	0.416116i	0.978116	−	0.208058i	$-0.0667143\pi$
$14$	−2.23193	−	3.00308i	−0.596509	−	0.802606i
$15$		0			0
$16$	3.41876	+	2.07655i	0.854690	+	0.519138i
$17$	0.214800	+	0.372045i	0.0520967	+	0.0902341i	0.890898	−	0.454204i	$-0.150076\pi$
$17$	0.214800	+	0.372045i	0.0520967	+	0.0902341i	−0.838801	+	0.544438i	$0.816743\pi$
$18$		0			0
$19$	−4.32799	−	2.49877i	−0.992909	−	0.573256i	−0.0867663	−	0.996229i	$-0.527653\pi$
$19$	−4.32799	−	2.49877i	−0.992909	−	0.573256i	−0.906143	+	0.422973i	$0.860987\pi$
$20$	4.73929	+	4.84589i	1.05974	+	1.08357i
$21$		0			0
$22$	−0.141056	+	0.0575103i	−0.0300732	+	0.0122612i
$23$	−4.56401	+	7.90510i	−0.951663	+	1.64833i	−0.209836	+	0.977737i	$0.567293\pi$
$23$	−4.56401	+	7.90510i	−0.951663	+	1.64833i	−0.741827	+	0.670591i	$0.766040\pi$
$24$		0			0
$25$	3.24294	+	5.61694i	0.648588	+	1.12339i
$26$	0.288642	−	2.10206i	0.0566074	−	0.412248i
$27$		0			0
$28$	−2.54934	−	4.63690i	−0.481780	−	0.876292i
$29$		−	7.95437i		−	1.47709i	−0.674204	−	0.738545i	$-0.735513\pi$
$29$		−	7.95437i		−	1.47709i	0.674204	−	0.738545i	$-0.264487\pi$
$30$		0			0
$31$	−0.393116	−	0.680897i	−0.0706058	−	0.122293i	0.828561	−	0.559899i	$-0.189160\pi$
$31$	−0.393116	−	0.680897i	−0.0706058	−	0.122293i	−0.899167	+	0.437606i	$0.855827\pi$
$32$	4.39041	+	3.56711i	0.776123	+	0.630582i
$33$		0			0
$34$	0.229373	+	0.562584i	0.0393371	+	0.0964823i
$35$	−2.23582	−	8.68345i	−0.377923	−	1.46777i
$36$		0			0
$37$	7.68900	+	4.43925i	1.26406	+	0.729808i	0.973858	−	0.227156i	$-0.0729429\pi$
$37$	7.68900	+	4.43925i	1.26406	+	0.729808i	0.290206	+	0.956964i	$0.406276\pi$
$38$	−5.58307	−	4.33358i	−0.905694	−	0.703000i
$39$		0			0
$40$	5.70777	+	7.70119i	0.902478	+	1.21767i
$41$	−8.59425			−1.34220			−0.671098	−	0.741369i	$-0.734177\pi$
$41$	−8.59425			−1.34220			−0.671098	+	0.741369i	$0.734177\pi$
$42$		0			0
$43$		−	6.65201i		−	1.01442i	−0.861822	−	0.507211i	$-0.830676\pi$
$43$		−	6.65201i		−	1.01442i	0.861822	−	0.507211i	$-0.169324\pi$
$44$	−0.208692	+	0.0534386i	−0.0314616	+	0.00805617i
$45$		0			0
$46$	−7.91532	+	10.1975i	−1.16705	+	1.50354i
$47$	2.87493	−	4.97953i	0.419352	−	0.726339i	−0.576523	−	0.817081i	$-0.695591\pi$
$47$	2.87493	−	4.97953i	0.419352	−	0.726339i	0.995874	+	0.0907426i	$0.0289241\pi$
$48$		0			0
$49$	−0.137086	+	6.99866i	−0.0195838	+	0.999808i
$50$	3.46295	+	8.49360i	0.489736	+	1.20118i
$51$		0			0
$52$	0.808814	−	2.88960i	0.112162	−	0.400715i
$53$	−0.286078	+	0.165167i	−0.0392959	+	0.0226875i	−0.519519	−	0.854459i	$-0.673889\pi$
$53$	−0.286078	+	0.165167i	−0.0392959	+	0.0226875i	0.480223	+	0.877146i	$0.340556\pi$
$54$		0			0
$55$	−0.365048			−0.0492230
$56$	−2.67972	−	6.98707i	−0.358092	−	0.933686i
$57$		0			0
$58$	1.53031	−	11.1446i	0.200939	−	1.46336i
$59$	−8.63850	+	4.98744i	−1.12464	+	0.649310i	−0.942581	−	0.333978i	$-0.891609\pi$
$59$	−8.63850	+	4.98744i	−1.12464	+	0.649310i	−0.182057	+	0.983288i	$0.558275\pi$
$60$		0			0
$61$	−1.76996	−	1.02189i	−0.226620	−	0.130839i	0.382392	−	0.924000i	$-0.375100\pi$
$61$	−1.76996	−	1.02189i	−0.226620	−	0.130839i	−0.609012	+	0.793161i	$0.708434\pi$
$62$	−0.419787	−	1.02961i	−0.0533130	−	0.130761i
$63$		0			0
$64$	5.46500	+	5.84241i	0.683125	+	0.730302i
$65$	2.54237	−	4.40351i	0.315342	−	0.546189i
$66$		0			0
$67$	2.79312	−	1.61261i	0.341234	−	0.197012i	−0.319583	−	0.947558i	$-0.603543\pi$
$67$	2.79312	−	1.61261i	0.341234	−	0.197012i	0.660818	+	0.750546i	$0.270210\pi$
$68$	0.213134	+	0.832346i	0.0258462	+	0.100937i
$69$		0			0
$70$	−1.46196	−	12.5962i	−0.174738	−	1.50554i
$71$	8.72656			1.03565			0.517826	−	0.855486i	$-0.326742\pi$
$71$	8.72656			1.03565			0.517826	+	0.855486i	$0.326742\pi$
$72$		0			0
$73$	−4.38649	−	7.59762i	−0.513399	−	0.889234i	−0.999879	−	0.0155420i	$-0.995053\pi$
$73$	−4.38649	−	7.59762i	−0.513399	−	0.889234i	0.486480	−	0.873692i	$-0.338281\pi$
$74$	9.91876	+	7.69894i	1.15303	+	0.894983i
$75$		0			0
$76$	−6.98854	−	7.14574i	−0.801640	−	0.819673i
$77$	0.274535	+	0.0764506i	0.0312862	+	0.00871236i
$78$		0			0
$79$	−0.785733	+	1.36093i	−0.0884018	+	0.153116i	−0.906836	−	0.421484i	$-0.861509\pi$
$79$	−0.785733	+	1.36093i	−0.0884018	+	0.153116i	0.818434	+	0.574601i	$0.194843\pi$
$80$	6.51537	+	11.8880i	0.728440	+	1.32912i
$81$		0			0
$82$	−12.0411	−	1.65341i	−1.32972	−	0.182589i
$83$		−	1.33259i		−	0.146271i	−0.997322	−	0.0731355i	$-0.976699\pi$
$83$		−	1.33259i		−	0.146271i	0.997322	−	0.0731355i	$-0.0233006\pi$
$84$		0			0
$85$			1.45595i			0.157920i
$86$	1.27975	−	9.31991i	0.137999	−	1.00499i
$87$		0			0
$88$	−0.302673	+	0.0347215i	−0.0322650	+	0.00370133i
$89$	−3.62404	+	6.27701i	−0.384147	+	0.665362i	−0.991650	−	0.128955i	$-0.958838\pi$
$89$	−3.62404	+	6.27701i	−0.384147	+	0.665362i	0.607503	+	0.794317i	$0.292171\pi$
$90$		0			0
$91$	−2.83421	+	2.77924i	−0.297106	+	0.291343i
$92$	−13.0517	+	12.7646i	−1.36074	+	1.33080i
$93$		0			0
$94$	4.98596	−	6.42355i	0.514263	−	0.662539i
$95$	−8.46852	−	14.6679i	−0.868852	−	1.50490i
$96$		0			0
$97$	−19.0450			−1.93373			−0.966864	−	0.255293i	$-0.917828\pi$
$97$	−19.0450			−1.93373			−0.966864	+	0.255293i	$0.917828\pi$
$98$	−1.53851	+	9.77921i	−0.155413	+	0.987850i
$99$		0			0
$100$	3.21778	+	12.5663i	0.321778	+	1.25663i
$101$	−2.88397	+	1.66506i	−0.286966	+	0.165680i	−0.636573	−	0.771217i	$-0.719649\pi$
$101$	−2.88397	+	1.66506i	−0.286966	+	0.165680i	0.349607	+	0.936897i	$0.386315\pi$
$102$		0			0
$103$	6.53174	−	11.3133i	0.643591	−	1.11473i	−0.341034	−	0.940051i	$-0.610777\pi$
$103$	6.53174	−	11.3133i	0.643591	−	1.11473i	0.984625	−	0.174682i	$-0.0558896\pi$
$104$	1.68912	−	3.89291i	0.165632	−	0.381732i
$105$		0			0
$106$	−0.432591	+	0.176373i	−0.0420169	+	0.0171309i
$107$	−4.00887	−	2.31452i	−0.387552	−	0.223753i	0.293547	−	0.955945i	$-0.405164\pi$
$107$	−4.00887	−	2.31452i	−0.387552	−	0.223753i	−0.681099	+	0.732191i	$0.738498\pi$
$108$		0			0
$109$	10.3011	−	5.94737i	0.986670	−	0.569654i	0.0823930	−	0.996600i	$-0.473744\pi$
$109$	10.3011	−	5.94737i	0.986670	−	0.569654i	0.904277	+	0.426946i	$0.140410\pi$
$110$	−0.511456	−	0.0702301i	−0.0487654	−	0.00669617i
$111$		0			0
$112$	−2.41025	−	10.3049i	−0.227747	−	0.973720i
$113$	−11.2752			−1.06068			−0.530339	−	0.847786i	$-0.677935\pi$
$113$	−11.2752			−1.06068			−0.530339	+	0.847786i	$0.677935\pi$
$114$		0			0
$115$	−26.7910	+	15.4678i	−2.49828	+	1.44238i
$116$	4.28813	−	15.3199i	0.398143	−	1.42242i
$117$		0			0
$118$	−13.0626	+	5.32581i	−1.20251	+	0.490281i
$119$	0.304914	−	1.09495i	0.0279515	−	0.100374i
$120$		0			0
$121$	−5.49420	+	9.51623i	−0.499473	+	0.865112i
$122$	−2.28323	−	1.77225i	−0.206714	−	0.160452i
$123$		0			0
$124$	−0.390067	−	1.52332i	−0.0350290	−	0.136798i
$125$			5.03577i			0.450413i
$126$		0			0
$127$	−8.12185			−0.720698			−0.360349	−	0.932818i	$-0.617342\pi$
$127$	−8.12185			−0.720698			−0.360349	+	0.932818i	$0.617342\pi$
$128$	6.53283	+	9.23700i	0.577426	+	0.816443i
$129$		0			0
$130$	4.40920	−	5.68050i	0.386713	−	0.498213i
$131$	9.73136	+	5.61840i	0.850233	+	0.490882i	0.860729	−	0.509063i	$-0.170008\pi$
$131$	9.73136	+	5.61840i	0.850233	+	0.490882i	−0.0104965	+	0.999945i	$0.503341\pi$
$132$		0			0
$133$	3.29693	+	12.8046i	0.285880	+	1.11030i
$134$	4.22359	−	1.72202i	0.364863	−	0.148760i
$135$		0			0
$136$	0.138483	+	1.20718i	0.0118748	+	0.103514i
$137$	3.21986	+	5.57695i	0.275091	+	0.476471i	0.970158	−	0.242473i	$-0.0779587\pi$
$137$	3.21986	+	5.57695i	0.275091	+	0.476471i	−0.695067	+	0.718945i	$0.744625\pi$
$138$		0			0
$139$		−	11.2139i		−	0.951154i	−0.879674	−	0.475577i	$-0.842239\pi$
$139$		−	11.2139i		−	0.951154i	0.879674	−	0.475577i	$-0.157761\pi$
$140$	0.375035	−	17.9294i	0.0316963	−	1.51531i
$141$		0			0
$142$	12.2265	+	1.67887i	1.02602	+	0.140887i
$143$	0.0808023	+	0.139954i	0.00675703	+	0.0117035i
$144$		0			0
$145$	13.4790	−	23.3463i	1.11937	−	1.93881i
$146$	−4.68408	−	11.4887i	−0.387658	−	0.950809i
$147$		0			0
$148$	12.4157	+	12.6950i	1.02056	+	1.04352i
$149$	12.9641	+	7.48481i	1.06206	+	0.613180i	0.926001	−	0.377521i	$-0.123224\pi$
$149$	12.9641	+	7.48481i	1.06206	+	0.613180i	0.136057	+	0.990701i	$0.456557\pi$
$150$		0			0
$151$	6.69597	+	11.5978i	0.544910	+	0.943813i	0.998613	+	0.0526591i	$0.0167697\pi$
$151$	6.69597	+	11.5978i	0.544910	+	0.943813i	−0.453702	+	0.891153i	$0.649897\pi$
$152$	−8.41667	−	11.3562i	−0.682682	−	0.921106i
$153$		0			0
$154$	0.369934	+	0.159929i	0.0298102	+	0.0128875i
$155$		−	2.66461i		−	0.214026i
$156$		0			0
$157$	16.2361	−	9.37390i	1.29578	−	0.748118i	0.316107	−	0.948724i	$-0.397624\pi$
$157$	16.2361	−	9.37390i	1.29578	−	0.748118i	0.979672	+	0.200605i	$0.0642908\pi$
$158$	−1.36269	+	1.75559i	−0.108410	+	0.139667i
$159$		0			0
$160$	6.84138	+	17.9093i	0.540859	+	1.41586i
$161$	23.3877	−	6.02188i	1.84321	−	0.474590i
$162$		0			0
$163$	2.21699	+	1.27998i	0.173648	+	0.100256i	0.584305	−	0.811534i	$-0.301367\pi$
$163$	2.21699	+	1.27998i	0.173648	+	0.100256i	−0.410657	+	0.911790i	$0.634701\pi$
$164$	−16.5523	−	4.63308i	−1.29252	−	0.361783i
$165$		0			0
$166$	0.256372	−	1.86705i	0.0198983	−	0.144911i
$167$	−5.88750			−0.455589			−0.227794	−	0.973709i	$-0.573151\pi$
$167$	−5.88750			−0.455589			−0.227794	+	0.973709i	$0.573151\pi$
$168$		0			0
$169$	10.7490			0.826847
$170$	−0.280104	+	2.03988i	−0.0214830	+	0.156452i
$171$		0			0
$172$	3.58604	−	12.8116i	0.273433	−	0.976876i
$173$	6.54988	+	3.78157i	0.497978	+	0.287508i	0.727878	−	0.685707i	$-0.240507\pi$
$173$	6.54988	+	3.78157i	0.497978	+	0.287508i	−0.229900	+	0.973214i	$0.573840\pi$
$174$		0			0
$175$	4.60344	−	16.5310i	0.347987	−	1.24963i
$176$	−0.430745	−	0.00958285i	−0.0324686	−	0.000722335i
$177$		0			0
$178$	−6.28513	+	8.09730i	−0.471090	+	0.606918i
$179$	9.76120	−	5.63563i	0.729586	−	0.421227i	−0.0886845	−	0.996060i	$-0.528266\pi$
$179$	9.76120	−	5.63563i	0.729586	−	0.421227i	0.818271	+	0.574833i	$0.194933\pi$
$180$		0			0
$181$			13.7298i			1.02053i	0.860018	+	0.510264i	$0.170452\pi$
$181$			13.7298i			1.02053i	−0.860018	+	0.510264i	$0.829548\pi$
$182$	−4.50560	+	3.34864i	−0.333978	+	0.248217i
$183$		0			0
$184$	−20.7421	+	15.3731i	−1.52913	+	1.13332i
$185$	15.0450	+	26.0587i	1.10613	+	1.91587i
$186$		0			0
$187$	−0.0400740	−	0.0231367i	−0.00293050	−	0.00169192i
$188$	8.22146	−	8.04059i	0.599612	−	0.586421i
$189$		0			0
$190$	−9.04306	−	22.1799i	−0.656053	−	1.60910i
$191$	−9.69930	+	16.7997i	−0.701816	+	1.21558i	0.266012	+	0.963970i	$0.414294\pi$
$191$	−9.69930	+	16.7997i	−0.701816	+	1.21558i	−0.967828	+	0.251612i	$0.919039\pi$
$192$		0			0
$193$	−1.27891	−	2.21513i	−0.0920577	−	0.159449i	0.816319	−	0.577601i	$-0.196011\pi$
$193$	−1.27891	−	2.21513i	−0.0920577	−	0.159449i	−0.908377	+	0.418153i	$0.862678\pi$
$194$	−26.6833	−	3.66399i	−1.91575	−	0.263059i
$195$		0			0
$196$	−4.03694	+	13.4053i	−0.288353	+	0.957524i
$197$		−	3.83452i		−	0.273199i	−0.990626	−	0.136599i	$-0.956383\pi$
$197$		−	3.83452i		−	0.273199i	0.990626	−	0.136599i	$-0.0436173\pi$
$198$		0			0
$199$	8.53263	+	14.7789i	0.604862	+	1.04765i	0.992073	+	0.125661i	$0.0401051\pi$
$199$	8.53263	+	14.7789i	0.604862	+	1.04765i	−0.387211	+	0.921991i	$0.626562\pi$
$200$	2.09074	+	18.2253i	0.147838	+	1.28872i
$201$		0			0
$202$	−4.36097	+	1.77803i	−0.306837	+	0.125102i
$203$	−15.0263	+	14.7348i	−1.05464	+	1.03418i
$204$		0			0
$205$	−25.2244	−	14.5633i	−1.76175	−	1.01715i
$206$	11.3279	−	14.5941i	0.789254	−	1.01682i
$207$		0			0
$208$	3.11551	−	5.12927i	0.216022	−	0.355651i
$209$	0.538298			0.0372349
$210$		0			0
$211$			12.8602i			0.885331i	0.896687	+	0.442666i	$0.145967\pi$
$211$			12.8602i			0.885331i	−0.896687	+	0.442666i	$0.854033\pi$
$212$	−0.640020	+	0.163886i	−0.0439568	+	0.0112557i
$213$		0			0
$214$	−5.17141	−	4.01405i	−0.353510	−	0.274395i
$215$	11.2721	−	19.5239i	0.768751	−	1.33152i
$216$		0			0
$217$	−0.558039	+	2.00393i	−0.0378822	+	0.136035i
$218$	15.5768	−	6.35086i	1.05499	−	0.430135i
$219$		0			0
$220$	−0.703073	−	0.196794i	−0.0474012	−	0.0132678i
$221$	0.558189	−	0.322271i	0.0375479	−	0.0216783i
$222$		0			0
$223$	12.1122			0.811092			0.405546	−	0.914075i	$-0.367081\pi$
$223$	12.1122			0.811092			0.405546	+	0.914075i	$0.367081\pi$
$224$	−1.39440	−	14.9015i	−0.0931675	−	0.995650i
$225$		0			0
$226$	−15.7973	−	2.16918i	−1.05082	−	0.144292i
$227$	6.00730	−	3.46832i	0.398719	−	0.230200i	−0.287212	−	0.957867i	$-0.592729\pi$
$227$	6.00730	−	3.46832i	0.398719	−	0.230200i	0.685931	+	0.727667i	$0.259395\pi$
$228$		0			0
$229$	7.60363	+	4.38996i	0.502462	+	0.290096i	0.729730	−	0.683736i	$-0.239646\pi$
$229$	7.60363	+	4.38996i	0.502462	+	0.290096i	−0.227268	+	0.973832i	$0.572979\pi$
$230$	−40.5118	+	16.5172i	−2.67127	+	1.08911i
$231$		0			0
$232$	8.95530	−	20.6393i	0.587944	−	1.35503i
$233$	8.20486	−	14.2112i	0.537518	−	0.931008i	−0.461519	−	0.887130i	$-0.652695\pi$
$233$	8.20486	−	14.2112i	0.537518	−	0.931008i	0.999037	−	0.0438780i	$-0.0139713\pi$
$234$		0			0
$235$	16.8760	−	9.74338i	1.10087	−	0.635588i
$236$	−19.3262	+	4.94875i	−1.25803	+	0.322136i
$237$		0			0
$238$	0.637859	−	1.47544i	0.0413463	−	0.0956386i
$239$	0.816406			0.0528089			0.0264045	−	0.999651i	$-0.491594\pi$
$239$	0.816406			0.0528089			0.0264045	+	0.999651i	$0.491594\pi$
$240$		0			0
$241$	12.0303	+	20.8371i	0.774939	+	1.34223i	0.934829	+	0.355099i	$0.115553\pi$
$241$	12.0303	+	20.8371i	0.774939	+	1.34223i	−0.159890	+	0.987135i	$0.551114\pi$
$242$	−9.52853	+	12.2759i	−0.612517	+	0.789123i
$243$		0			0
$244$	−2.85801	−	2.92230i	−0.182965	−	0.187081i
$245$	−12.2619	+	20.3090i	−0.783382	+	1.29749i
$246$		0			0
$247$	−3.74897	+	6.49341i	−0.238541	+	0.413166i
$248$	−0.253444	−	2.20931i	−0.0160937	−	0.140291i
$249$		0			0
$250$	−0.968811	+	7.05544i	−0.0612730	+	0.446225i
$251$			3.97637i			0.250986i	0.992094	+	0.125493i	$0.0400513\pi$
$251$			3.97637i			0.250986i	−0.992094	+	0.125493i	$0.959949\pi$
$252$		0			0
$253$		−	0.983206i		−	0.0618136i
$254$	−11.3793	−	1.56253i	−0.713998	−	0.0980419i
$255$		0			0
$256$	7.37586	+	14.1985i	0.460991	+	0.887405i
$257$	10.6451	−	18.4379i	0.664026	−	1.15013i	−0.315523	−	0.948918i	$-0.602180\pi$
$257$	10.6451	−	18.4379i	0.664026	−	1.15013i	0.979548	−	0.201208i	$-0.0644869\pi$
$258$		0			0
$259$	−5.85726	−	22.7483i	−0.363952	−	1.41351i
$260$	7.27044	−	7.11049i	0.450893	−	0.440974i
$261$		0			0
$262$	12.5534	+	9.74393i	0.775550	+	0.601982i
$263$	3.77491	+	6.53833i	0.232771	+	0.403171i	0.958623	−	0.284680i	$-0.0918874\pi$
$263$	3.77491	+	6.53833i	0.232771	+	0.403171i	−0.725852	+	0.687851i	$0.758554\pi$
$264$		0			0
$265$	−1.11953			−0.0687723
$266$	2.15580	+	18.5744i	0.132181	+	1.13887i
$267$		0			0
$268$	6.24883	−	1.60010i	0.381708	−	0.0977416i
$269$	−5.16933	+	2.98451i	−0.315179	+	0.181969i	−0.649242	−	0.760582i	$-0.724914\pi$
$269$	−5.16933	+	2.98451i	−0.315179	+	0.181969i	0.334062	+	0.942551i	$0.391580\pi$
$270$		0			0
$271$	−2.38737	+	4.13504i	−0.145022	+	0.251186i	−0.929381	−	0.369121i	$-0.879659\pi$
$271$	−2.38737	+	4.13504i	−0.145022	+	0.251186i	0.784359	+	0.620307i	$0.212992\pi$
$272$	−0.0382201	+	1.71798i	−0.00231743	+	0.104168i
$273$		0			0
$274$	3.43831	+	8.43314i	0.207716	+	0.509465i
$275$	−0.605016	−	0.349306i	−0.0364838	−	0.0210640i
$276$		0			0
$277$	−7.59525	+	4.38512i	−0.456354	+	0.263476i	−0.710510	−	0.703687i	$-0.751536\pi$
$277$	−7.59525	+	4.38512i	−0.456354	+	0.263476i	0.254156	+	0.967163i	$0.418202\pi$
$278$	2.15740	−	15.7115i	0.129393	−	0.942311i
$279$		0			0
$280$	3.97482	−	25.0482i	0.237541	−	1.49691i
$281$	−13.7147			−0.818151			−0.409076	−	0.912500i	$-0.634149\pi$
$281$	−13.7147			−0.818151			−0.409076	+	0.912500i	$0.634149\pi$
$282$		0			0
$283$	7.19449	−	4.15374i	0.427668	−	0.246914i	−0.270685	−	0.962668i	$-0.587250\pi$
$283$	7.19449	−	4.15374i	0.427668	−	0.246914i	0.698353	+	0.715754i	$0.253917\pi$
$284$	16.8071	+	4.70441i	0.997320	+	0.279155i
$285$		0			0
$286$	0.0862843	+	0.211630i	0.00510210	+	0.0125139i
$287$	15.9202	+	16.2350i	0.939737	+	0.958324i
$288$		0			0
$289$	8.40772	−	14.5626i	0.494572	−	0.856624i
$290$	23.3765	−	30.1166i	1.37272	−	1.76851i
$291$		0			0
$292$	−4.35246	−	16.9975i	−0.254708	−	0.994706i
$293$		−	9.10732i		−	0.532056i	−0.963965	−	0.266028i	$-0.914289\pi$
$293$		−	9.10732i		−	0.532056i	0.963965	−	0.266028i	$-0.0857113\pi$
$294$		0			0
$295$	−33.8057			−1.96824
$296$	14.9528	+	20.1751i	0.869117	+	1.17265i
$297$		0			0
$298$	16.7236	+	12.9808i	0.968769	+	0.751959i
$299$	11.8603	+	6.84752i	0.685896	+	0.396002i
$300$		0			0
$301$	−12.5660	+	12.3223i	−0.724295	+	0.710246i
$302$	7.15025	+	17.5374i	0.411451	+	1.00917i
$303$		0			0
$304$	−9.60754	−	17.5300i	−0.551030	−	1.00541i
$305$	−3.46326	−	5.99854i	−0.198306	−	0.343475i
$306$		0			0
$307$			20.1344i			1.14913i	0.818459	+	0.574565i	$0.194829\pi$
$307$			20.1344i			1.14913i	−0.818459	+	0.574565i	$0.805171\pi$
$308$	0.487534	+	0.295242i	0.0277799	+	0.0168230i
$309$		0			0
$310$	0.512633	−	3.73329i	0.0291156	−	0.212037i
$311$	1.60500	+	2.77995i	0.0910113	+	0.157636i	0.907937	−	0.419107i	$-0.137657\pi$
$311$	1.60500	+	2.77995i	0.0910113	+	0.157636i	−0.816926	+	0.576743i	$0.804323\pi$
$312$		0			0
$313$	−9.04356	+	15.6639i	−0.511172	+	0.885376i	0.488744	+	0.872427i	$0.337455\pi$
$313$	−9.04356	+	15.6639i	−0.511172	+	0.885376i	−0.999916	+	0.0129488i	$0.995878\pi$
$314$	24.5512	−	10.0099i	1.38551	−	0.564889i
$315$		0			0
$316$	−2.24697	+	2.19753i	−0.126402	+	0.123621i
$317$	−15.1458	−	8.74443i	−0.850673	−	0.491136i	0.0102048	−	0.999948i	$-0.496752\pi$
$317$	−15.1458	−	8.74443i	−0.850673	−	0.491136i	−0.860878	+	0.508812i	$0.830085\pi$
$318$		0			0
$319$	0.428394	+	0.742000i	0.0239855	+	0.0415440i
$320$	6.13973	+	26.4083i	0.343221	+	1.47627i
$321$		0			0
$322$	33.9262	−	3.93759i	1.89063	−	0.219433i
$323$		−	2.14694i		−	0.119459i
$324$		0			0
$325$	8.42725	−	4.86548i	0.467460	−	0.269888i
$326$	2.85989	+	2.21985i	0.158395	+	0.122946i
$327$		0			0
$328$	−22.2996	−	9.67569i	−1.23129	−	0.534251i
$329$	−14.7322	+	3.79326i	−0.812212	+	0.209129i
$330$		0			0
$331$	26.7076	+	15.4196i	1.46798	+	0.847541i	0.999357	−	0.0358560i	$-0.0114158\pi$
$331$	26.7076	+	15.4196i	1.46798	+	0.847541i	0.468626	+	0.883397i	$0.344749\pi$
$332$	0.718389	−	2.56654i	0.0394267	−	0.140857i
$333$		0			0
$334$	−8.24878	−	1.13267i	−0.451353	−	0.0619771i
$335$	10.9305			0.597199
$336$		0			0
$337$	8.73833			0.476007			0.238004	−	0.971264i	$-0.423507\pi$
$337$	8.73833			0.476007			0.238004	+	0.971264i	$0.423507\pi$
$338$	15.0601	+	2.06796i	0.819161	+	0.112482i
$339$		0			0
$340$	−0.784890	+	2.80412i	−0.0425666	+	0.152075i
$341$	0.0733414	+	0.0423437i	0.00397166	+	0.00229304i
$342$		0			0
$343$	13.4748	−	12.7055i	0.727572	−	0.686032i
$344$	7.48906	−	17.2600i	0.403783	−	0.930598i
$345$		0			0
$346$	8.44929	+	6.55834i	0.454237	+	0.352579i
$347$	−10.5626	+	6.09832i	−0.567030	+	0.327375i	−0.755962	−	0.654615i	$-0.772831\pi$
$347$	−10.5626	+	6.09832i	−0.567030	+	0.327375i	0.188932	+	0.981990i	$0.439497\pi$
$348$		0			0
$349$			5.25279i			0.281175i	0.990068	+	0.140588i	$0.0448992\pi$
$349$			5.25279i			0.281175i	−0.990068	+	0.140588i	$0.955101\pi$
$350$	9.63006	−	22.2754i	0.514748	−	1.19067i
$351$		0			0
$352$	−0.601658	−	0.0962955i	−0.0320685	−	0.00513257i
$353$	−8.73713	−	15.1332i	−0.465031	−	0.805457i	0.534172	−	0.845376i	$-0.320623\pi$
$353$	−8.73713	−	15.1332i	−0.465031	−	0.805457i	−0.999203	+	0.0399190i	$0.987290\pi$
$354$		0			0
$355$	25.6127	+	14.7875i	1.35938	+	0.784839i
$356$	−10.3637	+	10.1357i	−0.549274	+	0.537190i
$357$		0			0
$358$	14.7603	−	6.01798i	0.780107	−	0.318060i
$359$	2.13512	−	3.69813i	0.112687	−	0.195180i	−0.804166	−	0.594405i	$-0.797388\pi$
$359$	2.13512	−	3.69813i	0.112687	−	0.195180i	0.916853	+	0.399225i	$0.130721\pi$
$360$		0			0
$361$	2.98766	+	5.17478i	0.157245	+	0.272357i
$362$	−2.64142	+	19.2364i	−0.138830	+	1.01104i
$363$		0			0
$364$	−6.95688	+	3.82485i	−0.364640	+	0.200476i
$365$		−	29.7323i		−	1.55626i
$366$		0			0
$367$	3.14646	+	5.44983i	0.164244	+	0.284479i	0.936386	−	0.350971i	$-0.114148\pi$
$367$	3.14646	+	5.44983i	0.164244	+	0.284479i	−0.772143	+	0.635449i	$0.780815\pi$
$368$	−32.0186	+	17.5482i	−1.66909	+	0.914766i
$369$		0			0
$370$	16.0657	+	39.4044i	0.835215	+	2.04854i
$371$	0.841948	+	0.234460i	0.0437118	+	0.0121725i
$372$		0			0
$373$	−29.3109	−	16.9227i	−1.51766	−	0.876222i	−0.999784	−	0.0207662i	$-0.993389\pi$
$373$	−29.3109	−	16.9227i	−1.51766	−	0.876222i	−0.517876	−	0.855456i	$-0.673277\pi$
$374$	−0.0516951	−	0.0401258i	−0.00267309	−	0.00207485i
$375$		0			0
$376$	13.0657	−	9.68371i	0.673813	−	0.499399i
$377$	−11.9342			−0.614641
$378$		0			0
$379$		−	2.56918i		−	0.131970i	−0.997821	−	0.0659850i	$-0.978981\pi$
$379$		−	2.56918i		−	0.131970i	0.997821	−	0.0659850i	$-0.0210190\pi$
$380$	−8.40282	−	32.8153i	−0.431056	−	1.68339i
$381$		0			0
$382$	−16.8214	+	21.6715i	−0.860657	+	1.10881i
$383$	4.40880	−	7.63626i	0.225279	−	0.390195i	−0.731124	−	0.682244i	$-0.761004\pi$
$383$	4.40880	−	7.63626i	0.225279	−	0.390195i	0.956403	+	0.292050i	$0.0943373\pi$
$384$		0			0
$385$	0.676221	+	0.689596i	0.0344634	+	0.0351451i
$386$	−1.36567	−	3.34959i	−0.0695109	−	0.170490i
$387$		0			0
$388$	−36.6802	−	10.2670i	−1.86216	−	0.521228i
$389$	−11.2701	+	6.50678i	−0.571416	+	0.329907i	−0.757715	−	0.652586i	$-0.773684\pi$
$389$	−11.2701	+	6.50678i	−0.571416	+	0.329907i	0.186299	+	0.982493i	$0.440351\pi$
$390$		0			0
$391$	−3.92140			−0.198314
$392$	−8.23502	+	18.0051i	−0.415931	+	0.909396i
$393$		0			0
$394$	0.737709	−	5.37242i	0.0371652	−	0.270659i
$395$	−4.61230	+	2.66291i	−0.232070	+	0.133986i
$396$		0			0
$397$	8.49061	+	4.90206i	0.426132	+	0.246027i	0.697697	−	0.716393i	$-0.254208\pi$
$397$	8.49061	+	4.90206i	0.426132	+	0.246027i	−0.271566	+	0.962420i	$0.587541\pi$
$398$	9.11152	+	22.3478i	0.456719	+	1.12020i
$399$		0			0
$400$	−0.577027	+	25.9371i	−0.0288514	+	1.29685i
$401$	−1.25638	+	2.17611i	−0.0627405	+	0.108670i	−0.895689	−	0.444680i	$-0.853317\pi$
$401$	−1.25638	+	2.17611i	−0.0627405	+	0.108670i	0.832949	+	0.553350i	$0.186651\pi$
$402$		0			0
$403$	−1.02157	+	0.589804i	−0.0508880	+	0.0293802i
$404$	−6.45208	+	1.65214i	−0.321003	+	0.0821973i
$405$		0			0
$406$	−23.8876	+	17.7536i	−1.18552	+	0.881098i
$407$	−0.956328			−0.0474034
$408$		0			0
$409$	−7.54163	−	13.0625i	−0.372910	−	0.645899i	0.617102	−	0.786883i	$-0.288307\pi$
$409$	−7.54163	−	13.0625i	−0.372910	−	0.645899i	−0.990012	+	0.140985i	$0.954973\pi$
$410$	−32.5393	−	25.2570i	−1.60700	−	1.24735i
$411$		0			0
$412$	18.6789	−	18.2679i	0.920242	−	0.899997i
$413$	25.4237	+	7.07981i	1.25102	+	0.348375i
$414$		0			0
$415$	2.25813	−	3.91120i	0.110847	−	0.191993i
$416$	5.35184	−	6.58706i	0.262396	−	0.322957i
$417$		0			0
$418$	0.754192	+	0.103561i	0.0368887	+	0.00506534i
$419$		−	18.2508i		−	0.891608i	−0.895130	−	0.445804i	$-0.852918\pi$
$419$		−	18.2508i		−	0.891608i	0.895130	−	0.445804i	$-0.147082\pi$
$420$		0			0
$421$		−	34.3633i		−	1.67476i	−0.546619	−	0.837382i	$-0.684085\pi$
$421$		−	34.3633i		−	1.67476i	0.546619	−	0.837382i	$-0.315915\pi$
$422$	−2.47412	+	18.0180i	−0.120438	+	0.877101i
$423$		0			0
$424$	−0.928241	+	0.106484i	−0.0450793	+	0.00517134i
$425$	−1.39317	+	2.41304i	−0.0675785	+	0.117049i
$426$		0			0
$427$	1.34830	+	5.23652i	0.0652490	+	0.253413i
$428$	−6.47324	−	6.61886i	−0.312896	−	0.319935i
$429$		0			0
$430$	19.5491	−	25.1856i	0.942741	−	1.21456i
$431$	12.8087	+	22.1854i	0.616974	+	1.06863i	0.990035	+	0.140824i	$0.0449751\pi$
$431$	12.8087	+	22.1854i	0.616974	+	1.06863i	−0.373060	+	0.927807i	$0.621692\pi$
$432$		0			0
$433$	3.79352			0.182305			0.0911525	−	0.995837i	$-0.470945\pi$
$433$	3.79352			0.182305			0.0911525	+	0.995837i	$0.470945\pi$
$434$	−1.16738	+	2.70028i	−0.0560359	+	0.129617i
$435$		0			0
$436$	23.0459	−	5.90123i	1.10370	−	0.282617i
$437$	39.5060	−	22.8088i	1.88983	−	1.09109i
$438$		0			0
$439$	−4.48040	+	7.76028i	−0.213838	+	0.370378i	−0.952912	−	0.303246i	$-0.901930\pi$
$439$	−4.48040	+	7.76028i	−0.213838	+	0.370378i	0.739075	+	0.673623i	$0.235263\pi$
$440$	−0.947191	−	0.410983i	−0.0451556	−	0.0195928i
$441$		0			0
$442$	0.844061	−	0.344135i	0.0401479	−	0.0163688i
$443$	11.5331	+	6.65864i	0.547954	+	0.316361i	0.748296	−	0.663365i	$-0.230872\pi$
$443$	11.5331	+	6.65864i	0.547954	+	0.316361i	−0.200342	+	0.979726i	$0.564205\pi$
$444$		0			0
$445$	−21.2733	+	12.2822i	−1.00845	+	0.582230i
$446$	16.9700	+	2.33021i	0.803552	+	0.110339i
$447$		0			0
$448$	0.913194	−	21.1463i	0.0431444	−	0.999069i
$449$	−26.7885			−1.26423			−0.632115	−	0.774875i	$-0.717813\pi$
$449$	−26.7885			−1.26423			−0.632115	+	0.774875i	$0.717813\pi$
$450$		0			0
$451$	0.801689	−	0.462855i	0.0377501	−	0.0217950i
$452$	−21.7157	−	6.07834i	−1.02142	−	0.285901i
$453$		0			0
$454$	9.08389	−	3.70362i	0.426328	−	0.173820i
$455$	−13.0280	+	3.35447i	−0.610763	+	0.157260i
$456$		0			0
$457$	−6.83952	+	11.8464i	−0.319939	+	0.554151i	−0.980475	−	0.196643i	$-0.936996\pi$
$457$	−6.83952	+	11.8464i	−0.319939	+	0.554151i	0.660536	+	0.750795i	$0.270329\pi$
$458$	9.80862	+	7.61345i	0.458327	+	0.355753i
$459$		0			0
$460$	−59.9375	+	15.3478i	−2.79460	+	0.715596i
$461$			28.1071i			1.30908i	0.756028	+	0.654539i	$0.227137\pi$
$461$			28.1071i			1.30908i	−0.756028	+	0.654539i	$0.772863\pi$
$462$		0			0
$463$	0.408558			0.0189873			0.00949365	−	0.999955i	$-0.496978\pi$
$463$	0.408558			0.0189873			0.00949365	+	0.999955i	$0.496978\pi$
$464$	16.5177	−	27.1941i	0.766814	−	1.26245i
$465$		0			0
$466$	14.2296	−	18.3324i	0.659173	−	0.849231i
$467$	14.6477	+	8.45683i	0.677813	+	0.391335i	0.799030	−	0.601291i	$-0.205347\pi$
$467$	14.6477	+	8.45683i	0.677813	+	0.391335i	−0.121218	+	0.992626i	$0.538680\pi$
$468$		0			0
$469$	−8.22035	−	2.28914i	−0.379580	−	0.105703i
$470$	25.5189	−	10.4044i	1.17710	−	0.479920i
$471$		0			0
$472$	−28.0294	+	3.21543i	−1.29016	+	0.148002i
$473$	0.358253	+	0.620513i	0.0164725	+	0.0285312i
$474$		0			0
$475$		−	32.4134i		−	1.48723i
$476$	1.17754	−	1.94447i	0.0539723	−	0.0891249i
$477$		0			0
$478$	1.14384	+	0.157065i	0.0523180	+	0.00718399i
$479$	−9.76658	−	16.9162i	−0.446247	−	0.772922i	0.551892	−	0.833916i	$-0.313906\pi$
$479$	−9.76658	−	16.9162i	−0.446247	−	0.772922i	−0.998138	+	0.0609941i	$0.980573\pi$
$480$		0			0
$481$	6.66033	−	11.5360i	0.303685	−	0.525998i
$482$	12.8465	+	31.5086i	0.585141	+	1.43518i
$483$		0			0
$484$	−15.7118	+	15.3662i	−0.714173	+	0.698461i
$485$	−55.8977	−	32.2725i	−2.53818	−	1.46542i
$486$		0			0
$487$	−17.8306	−	30.8834i	−0.807980	−	1.39946i	−0.914261	−	0.405126i	$-0.867228\pi$
$487$	−17.8306	−	30.8834i	−0.807980	−	1.39946i	0.106281	−	0.994336i	$-0.466106\pi$
$488$	−3.44205	−	4.64417i	−0.155814	−	0.210232i
$489$		0			0
$490$	−21.0869	+	26.0952i	−0.952607	+	1.17886i
$491$			19.3905i			0.875082i	0.899198	+	0.437541i	$0.144151\pi$
$491$			19.3905i			0.875082i	−0.899198	+	0.437541i	$0.855849\pi$
$492$		0			0
$493$	2.95938	−	1.70860i	0.133284	−	0.0769514i
$494$	−6.50180	+	8.37645i	−0.292530	+	0.376874i
$495$		0			0
$496$	0.0699485	−	3.14415i	0.00314078	−	0.141177i
$497$	−16.1652	−	16.4850i	−0.725110	−	0.739452i
$498$		0			0
$499$	−11.4791	−	6.62747i	−0.513876	−	0.296686i	0.220549	−	0.975376i	$-0.429215\pi$
$499$	−11.4791	−	6.62747i	−0.513876	−	0.296686i	−0.734425	+	0.678689i	$0.762548\pi$
$500$	−2.71474	+	9.69876i	−0.121407	+	0.433742i
$501$		0			0
$502$	−0.764997	+	5.57116i	−0.0341435	+	0.248653i
$503$	−24.7969			−1.10564			−0.552819	−	0.833302i	$-0.686448\pi$
$503$	−24.7969			−1.10564			−0.552819	+	0.833302i	$0.686448\pi$
$504$		0			0
$505$	−11.2861			−0.502223
$506$	0.189155	−	1.37754i	0.00840897	−	0.0612390i
$507$		0			0
$508$	−15.6425	−	4.37842i	−0.694023	−	0.194261i
$509$	−22.7230	−	13.1191i	−1.00718	−	0.581495i	−0.0968148	−	0.995302i	$-0.530865\pi$
$509$	−22.7230	−	13.1191i	−1.00718	−	0.581495i	−0.910365	+	0.413807i	$0.864199\pi$
$510$		0			0
$511$	−6.22673	+	22.3603i	−0.275455	+	0.989161i
$512$	7.60248	+	21.3120i	0.335985	+	0.941867i
$513$		0			0
$514$	18.4618	−	23.7848i	0.814313	−	1.04910i
$515$	38.3417	−	22.1366i	1.68954	−	0.975455i
$516$		0			0
$517$			0.619334i			0.0272383i
$518$	−3.82995	−	32.9988i	−0.168278	−	1.44988i
$519$		0			0
$520$	11.5543	−	8.56354i	0.506691	−	0.375536i
$521$	18.4536	+	31.9626i	0.808468	+	1.40031i	0.913925	+	0.405883i	$0.133036\pi$
$521$	18.4536	+	31.9626i	0.808468	+	1.40031i	−0.105457	+	0.994424i	$0.533631\pi$
$522$		0			0
$523$	3.36834	+	1.94471i	0.147287	+	0.0850364i	0.571833	−	0.820370i	$-0.306233\pi$
$523$	3.36834	+	1.94471i	0.147287	+	0.0850364i	−0.424545	+	0.905407i	$0.639566\pi$
$524$	15.7135	+	16.0670i	0.686449	+	0.701890i
$525$		0			0
$526$	4.03102	+	9.88688i	0.175761	+	0.431089i
$527$	0.168883	−	0.292514i	0.00735665	−	0.0127421i
$528$		0			0
$529$	−30.1604	−	52.2394i	−1.31132	−	2.27128i
$530$	−1.56854	−	0.215382i	−0.0681330	−	0.00935561i
$531$		0			0
$532$	−0.553026	+	26.4387i	−0.0239767	+	1.14626i
$533$			12.8942i			0.558510i
$534$		0			0
$535$	−7.84410	−	13.5864i	−0.339130	−	0.587391i
$536$	9.06286	−	1.03966i	0.391456	−	0.0449064i
$537$		0			0
$538$	−7.81675	+	3.18699i	−0.337004	+	0.137401i
$539$	−0.364135	−	0.660232i	−0.0156844	−	0.0284382i
$540$		0			0
$541$	−4.77290	−	2.75564i	−0.205203	−	0.118474i	0.393877	−	0.919163i	$-0.371134\pi$
$541$	−4.77290	−	2.75564i	−0.205203	−	0.118474i	−0.599080	+	0.800689i	$0.704467\pi$
$542$	−4.14039	+	5.33417i	−0.177845	+	0.229122i
$543$		0			0
$544$	−0.384063	+	2.39964i	−0.0164666	+	0.102884i
$545$	40.3122			1.72679
$546$		0			0
$547$		−	3.62706i		−	0.155082i	−0.996989	−	0.0775409i	$-0.975293\pi$
$547$		−	3.62706i		−	0.155082i	0.996989	−	0.0775409i	$-0.0247068\pi$
$548$	3.19488	+	12.4769i	0.136478	+	0.532986i
$549$		0			0
$550$	−0.780466	−	0.605798i	−0.0332792	−	0.0258313i
$551$	−19.8761	+	34.4264i	−0.846751	+	1.46662i
$552$		0			0
$553$	4.02638	−	1.03672i	0.171219	−	0.0440856i
$554$	−11.4851	+	4.68262i	−0.487954	+	0.198946i
$555$		0			0
$556$	6.04533	−	21.5978i	0.256379	−	0.915949i
$557$	9.16878	−	5.29360i	0.388494	−	0.224297i	−0.293014	−	0.956108i	$-0.594658\pi$
$557$	9.16878	−	5.29360i	0.388494	−	0.224297i	0.681507	+	0.731811i	$0.261325\pi$
$558$		0			0
$559$	−9.98021			−0.422118
$560$	10.3879	−	34.3294i	0.438969	−	1.45068i
$561$		0			0
$562$	−19.2152	−	2.63852i	−0.810545	−	0.111299i
$563$	−35.8149	+	20.6777i	−1.50942	+	0.871463i	−0.509478	+	0.860484i	$0.670161\pi$
$563$	−35.8149	+	20.6777i	−1.50942	+	0.871463i	−0.999940	+	0.0109787i	$0.996505\pi$
$564$		0			0
$565$	−33.0930	−	19.1062i	−1.39223	−	0.803805i
$566$	10.8791	−	4.43555i	0.457282	−	0.186440i
$567$		0			0
$568$	22.6428	+	9.82465i	0.950073	+	0.412233i
$569$	−17.7569	+	30.7559i	−0.744408	+	1.28935i	0.206063	+	0.978539i	$0.433935\pi$
$569$	−17.7569	+	30.7559i	−0.744408	+	1.28935i	−0.950471	+	0.310814i	$0.899398\pi$
$570$		0			0
$571$	−26.6337	+	15.3770i	−1.11459	+	0.643507i	−0.940013	−	0.341138i	$-0.889188\pi$
$571$	−26.6337	+	15.3770i	−1.11459	+	0.643507i	−0.174573	+	0.984644i	$0.555854\pi$
$572$	0.0801755	+	0.313107i	0.00335230	+	0.0130917i
$573$		0			0
$574$	19.1818	+	25.8092i	0.800633	+	1.07725i
$575$	−59.2033			−2.46895
$576$		0			0
$577$	0.00598449	+	0.0103654i	0.000249138	+	0.000431519i	0.866150	−	0.499784i	$-0.166587\pi$
$577$	0.00598449	+	0.0103654i	0.000249138	+	0.000431519i	−0.865901	+	0.500216i	$0.833254\pi$
$578$	14.5814	−	18.7856i	0.606507	−	0.781380i
$579$		0			0
$580$	38.5460	−	37.6980i	1.60054	−	1.56533i
$581$	−2.51735	+	2.46852i	−0.104437	+	0.102412i
$582$		0			0
$583$	0.0177907	−	0.0308143i	0.000736814	−	0.00127620i
$584$	−2.82799	−	24.6520i	−0.117023	−	1.02011i
$585$		0			0
$586$	1.75212	−	12.7600i	0.0723795	−	0.527109i
$587$		−	45.9133i		−	1.89505i	−0.319688	−	0.947523i	$-0.603578\pi$
$587$		−	45.9133i		−	1.89505i	0.319688	−	0.947523i	$-0.396422\pi$
$588$		0			0
$589$			3.92922i			0.161901i
$590$	−47.3640	−	6.50374i	−1.94995	−	0.267755i
$591$		0			0
$592$	17.0685	+	31.1433i	0.701512	+	1.27998i
$593$	20.1369	−	34.8781i	0.826923	−	1.43227i	−0.0735177	−	0.997294i	$-0.523423\pi$
$593$	20.1369	−	34.8781i	0.826923	−	1.43227i	0.900441	−	0.434979i	$-0.143244\pi$
$594$		0			0
$595$	2.75038	−	2.69703i	0.112754	−	0.110567i
$596$	20.9335	+	21.4044i	0.857469	+	0.876757i
$597$		0			0
$598$	15.2996	+	11.8756i	0.625649	+	0.485629i
$599$	−9.26440	−	16.0464i	−0.378533	−	0.655638i	0.612316	−	0.790613i	$-0.290238\pi$
$599$	−9.26440	−	16.0464i	−0.378533	−	0.655638i	−0.990849	+	0.134975i	$0.956905\pi$
$600$		0			0
$601$	−6.16213			−0.251358			−0.125679	−	0.992071i	$-0.540111\pi$
$601$	−6.16213			−0.251358			−0.125679	+	0.992071i	$0.540111\pi$
$602$	−19.9765	+	14.8469i	−0.814181	+	0.605113i
$603$		0			0
$604$	6.64402	+	25.9467i	0.270341	+	1.05576i
$605$	−32.2513	+	18.6203i	−1.31120	+	0.757023i
$606$		0			0
$607$	−21.4265	+	37.1119i	−0.869677	+	1.50632i	−0.00734959	+	0.999973i	$0.502339\pi$
$607$	−21.4265	+	37.1119i	−0.869677	+	1.50632i	−0.862327	+	0.506351i	$0.830994\pi$
$608$	−10.0883	−	26.4090i	−0.409134	−	1.07103i
$609$		0			0
$610$	−3.69822	−	9.07063i	−0.149737	−	0.367259i
$611$	−7.47093	−	4.31334i	−0.302241	−	0.174499i
$612$		0			0
$613$	−14.0140	+	8.09100i	−0.566021	+	0.326793i	−0.755559	−	0.655081i	$-0.772635\pi$
$613$	−14.0140	+	8.09100i	−0.566021	+	0.326793i	0.189537	+	0.981874i	$0.439301\pi$
$614$	−3.87357	+	28.2096i	−0.156325	+	1.13845i
$615$		0			0
$616$	0.626268	+	0.507448i	0.0252331	+	0.0204457i
$617$	19.0082			0.765240			0.382620	−	0.923906i	$-0.375022\pi$
$617$	19.0082			0.765240			0.382620	+	0.923906i	$0.375022\pi$
$618$		0			0
$619$	−13.0045	+	7.50818i	−0.522697	+	0.301779i	−0.738037	−	0.674760i	$-0.764247\pi$
$619$	−13.0045	+	7.50818i	−0.522697	+	0.301779i	0.215341	+	0.976539i	$0.430914\pi$
$620$	1.43647	−	5.13197i	0.0576899	−	0.206105i
$621$		0			0
$622$	1.71389	+	4.20367i	0.0687208	+	0.168552i
$623$	18.5709	−	4.78164i	0.744027	−	0.191573i
$624$		0			0
$625$	7.68139	−	13.3045i	0.307255	−	0.532182i
$626$	−15.6841	+	20.2063i	−0.626864	+	0.807607i
$627$		0			0
$628$	36.3236	−	9.30117i	1.44947	−	0.371157i
$629$			3.81420i			0.152082i
$630$		0			0
$631$	42.1434			1.67770			0.838852	−	0.544359i	$-0.183227\pi$
$631$	42.1434			1.67770			0.838852	+	0.544359i	$0.183227\pi$
$632$	−3.57092	+	2.64661i	−0.142044	+	0.105276i
$633$		0			0
$634$	−19.5380	−	15.1654i	−0.775952	−	0.602294i
$635$	−23.8379	−	13.7628i	−0.945978	−	0.546160i
$636$		0			0
$637$	10.5003	+	0.205675i	0.416037	+	0.00814913i
$638$	0.457458	+	1.12201i	0.0181109	+	0.0444207i
$639$		0			0
$640$	3.52158	+	38.1810i	0.139203	+	1.50924i
$641$	−14.4278	−	24.9896i	−0.569862	−	0.987030i	−0.996579	−	0.0826446i	$-0.973663\pi$
$641$	−14.4278	−	24.9896i	−0.569862	−	0.987030i	0.426717	−	0.904385i	$-0.359670\pi$
$642$		0			0
$643$		−	10.7484i		−	0.423876i	−0.977283	−	0.211938i	$-0.932022\pi$
$643$		−	10.7484i		−	0.423876i	0.977283	−	0.211938i	$-0.0679775\pi$
$644$	48.2904	+	1.01011i	1.90291	+	0.0398038i
$645$		0			0
$646$	0.413041	−	3.00801i	0.0162509	−	0.118348i
$647$	−6.75381	−	11.6979i	−0.265520	−	0.459894i	0.702180	−	0.711999i	$-0.252210\pi$
$647$	−6.75381	−	11.6979i	−0.265520	−	0.459894i	−0.967700	+	0.252106i	$0.918877\pi$
$648$		0			0
$649$	0.537211	−	0.930478i	0.0210874	−	0.0365244i
$650$	12.7432	−	5.19557i	0.499829	−	0.203787i
$651$		0			0
$652$	3.57983	+	3.66036i	0.140197	+	0.143351i
$653$	7.85026	+	4.53235i	0.307204	+	0.177364i	0.645675	−	0.763613i	$-0.276576\pi$
$653$	7.85026	+	4.53235i	0.307204	+	0.177364i	−0.338470	+	0.940977i	$0.609910\pi$
$654$		0			0
$655$	19.0412	+	32.9804i	0.744002	+	1.28865i
$656$	−29.3817	−	17.8464i	−1.14716	−	0.696785i
$657$		0			0
$658$	−21.3706	+	2.48034i	−0.833111	+	0.0966936i
$659$		−	31.5929i		−	1.23068i	−0.788261	−	0.615341i	$-0.789018\pi$
$659$		−	31.5929i		−	1.23068i	0.788261	−	0.615341i	$-0.210982\pi$
$660$		0			0
$661$	9.26579	−	5.34961i	0.360398	−	0.208076i	−0.308858	−	0.951108i	$-0.599947\pi$
$661$	9.26579	−	5.34961i	0.360398	−	0.208076i	0.669255	+	0.743033i	$0.266613\pi$
$662$	34.4526	+	26.7421i	1.33904	+	1.03936i
$663$		0			0
$664$	1.50028	−	3.45769i	0.0582221	−	0.134184i
$665$	−12.0213	+	43.1687i	−0.466166	+	1.67401i
$666$		0			0
$667$	62.8801	+	36.3039i	2.43473	+	1.40569i
$668$	−11.3392	−	3.17390i	−0.438726	−	0.122802i
$669$		0			0
$670$	15.3144	+	2.10288i	0.591647	+	0.0812414i
$671$	0.220141			0.00849843
$672$		0			0
$673$	21.8493			0.842230			0.421115	−	0.907007i	$-0.361639\pi$
$673$	21.8493			0.842230			0.421115	+	0.907007i	$0.361639\pi$
$674$	12.2430	+	1.68113i	0.471582	+	0.0647548i
$675$		0			0
$676$	20.7023	+	5.79470i	0.796244	+	0.222873i
$677$	3.24311	+	1.87241i	0.124643	+	0.0719625i	0.561025	−	0.827799i	$-0.310407\pi$
$677$	3.24311	+	1.87241i	0.124643	+	0.0719625i	−0.436382	+	0.899761i	$0.643740\pi$
$678$		0			0
$679$	35.2793	+	35.9771i	1.35390	+	1.38068i
$680$	−1.63916	+	3.77776i	−0.0628588	+	0.144871i
$681$		0			0
$682$	0.0946098	+	0.0734362i	0.00362280	+	0.00281202i
$683$	24.2667	−	14.0104i	0.928541	−	0.536093i	0.0421911	−	0.999110i	$-0.486566\pi$
$683$	24.2667	−	14.0104i	0.928541	−	0.536093i	0.886350	+	0.463016i	$0.153233\pi$
$684$		0			0
$685$			21.8247i			0.833880i
$686$	21.3235	−	15.2089i	0.814134	−	0.580677i
$687$		0			0
$688$	13.8133	−	22.7416i	0.526625	−	0.867017i
$689$	0.247806	+	0.429212i	0.00944064	+	0.0163517i
$690$		0			0
$691$	14.0726	+	8.12481i	0.535346	+	0.309082i	0.743191	−	0.669080i	$-0.233312\pi$
$691$	14.0726	+	8.12481i	0.535346	+	0.309082i	−0.207845	+	0.978162i	$0.566645\pi$
$692$	10.5763	+	10.8142i	0.402050	+	0.411094i
$693$		0			0
$694$	−15.9721	+	6.51205i	−0.606294	+	0.247194i
$695$	19.0025	−	32.9133i	0.720805	−	1.24847i
$696$		0			0
$697$	−1.84605	−	3.19744i	−0.0699240	−	0.121112i
$698$	−1.01056	+	7.35951i	−0.0382504	+	0.278561i
$699$		0			0
$700$	17.7778	−	29.3567i	0.671939	−	1.10958i
$701$			6.77821i			0.256010i	0.991774	+	0.128005i	$0.0408573\pi$
$701$			6.77821i			0.256010i	−0.991774	+	0.128005i	$0.959143\pi$
$702$		0			0
$703$	−22.1853	−	38.4260i	−0.836734	−	1.44927i
$704$	−0.824438	−	0.250667i	−0.0310722	−	0.00944737i
$705$		0			0
$706$	−9.32990	−	22.8835i	−0.351135	−	0.861230i
$707$	8.48773	+	2.36360i	0.319214	+	0.0888923i
$708$		0			0
$709$	18.2622	+	10.5437i	0.685851	+	0.395976i	0.802056	−	0.597249i	$-0.203740\pi$
$709$	18.2622	+	10.5437i	0.685851	+	0.395976i	−0.116205	+	0.993225i	$0.537073\pi$
$710$	33.0402	+	25.6458i	1.23998	+	0.962470i
$711$		0			0
$712$	−16.4702	+	12.2069i	−0.617246	+	0.457475i
$713$	7.17675			0.268772
$714$		0			0
$715$			0.547692i			0.0204825i
$716$	21.8380	−	5.59191i	0.816123	−	0.208979i
$717$		0			0
$718$	3.70291	−	4.77056i	0.138191	−	0.178036i
$719$	9.43045	−	16.3340i	0.351697	−	0.609156i	−0.634850	−	0.772635i	$-0.718938\pi$
$719$	9.43045	−	16.3340i	0.351697	−	0.609156i	0.986547	+	0.163479i	$0.0522715\pi$
$720$		0			0
$721$	−33.4710	+	8.61814i	−1.24653	+	0.320956i
$722$	3.19036	+	7.82499i	0.118733	+	0.291216i
$723$		0			0
$724$	−7.40162	+	26.4433i	−0.275079	+	0.982757i
$725$	44.6792	−	25.7955i	1.65934	−	0.958022i
$726$		0			0
$727$	−5.67246			−0.210380			−0.105190	−	0.994452i	$-0.533545\pi$
$727$	−5.67246			−0.210380			−0.105190	+	0.994452i	$0.533545\pi$
$728$	−10.4829	+	4.02046i	−0.388522	+	0.149008i
$729$		0			0
$730$	5.72008	−	41.6570i	0.211710	−	1.54179i
$731$	2.47485	−	1.42885i	0.0915355	−	0.0528480i
$732$		0			0
$733$	17.9878	+	10.3853i	0.664394	+	0.383588i	0.793949	−	0.607984i	$-0.208022\pi$
$733$	17.9878	+	10.3853i	0.664394	+	0.383588i	−0.129555	+	0.991572i	$0.541355\pi$
$734$	3.35993	+	8.24091i	0.124017	+	0.304177i
$735$		0			0
$736$	−48.2363	+	18.4263i	−1.77801	+	0.679203i
$737$	−0.173699	+	0.300855i	−0.00639828	+	0.0110821i
$738$		0			0
$739$	35.6239	−	20.5675i	1.31045	−	0.756586i	0.328276	−	0.944582i	$-0.393533\pi$
$739$	35.6239	−	20.5675i	1.31045	−	0.756586i	0.982170	+	0.187996i	$0.0601992\pi$
$740$	14.9283	+	58.2990i	0.548774	+	2.14311i
$741$		0			0
$742$	1.13452	+	0.490473i	0.0416495	+	0.0180058i
$743$	−2.47186			−0.0906839			−0.0453419	−	0.998972i	$-0.514438\pi$
$743$	−2.47186			−0.0906839			−0.0453419	+	0.998972i	$0.514438\pi$
$744$		0			0
$745$	25.3666	+	43.9363i	0.929362	+	1.60970i
$746$	−37.8108	−	29.3488i	−1.38435	−	1.07453i
$747$		0			0
$748$	−0.0647087	−	0.0661643i	−0.00236598	−	0.00241921i
$749$	3.05384	+	11.8605i	0.111585	+	0.433372i
$750$		0			0
$751$	−10.9291	+	18.9297i	−0.398808	+	0.690755i	−0.993579	−	0.113140i	$-0.963909\pi$
$751$	−10.9291	+	18.9297i	−0.398808	+	0.690755i	0.594771	+	0.803895i	$0.297243\pi$
$752$	20.1690	−	11.0539i	0.735486	−	0.403093i
$753$		0			0
$754$	−16.7206	−	2.29597i	−0.608927	−	0.0836142i
$755$			45.3864i			1.65178i
$756$		0			0
$757$		−	48.6072i		−	1.76666i	−0.468753	−	0.883329i	$-0.655297\pi$
$757$		−	48.6072i		−	1.76666i	0.468753	−	0.883329i	$-0.344703\pi$
$758$	0.494275	−	3.59960i	0.0179529	−	0.130743i
$759$		0			0
$760$	−5.45970	−	47.5931i	−0.198044	−	1.72638i
$761$	−3.92491	+	6.79815i	−0.142278	+	0.246433i	−0.928354	−	0.371697i	$-0.878776\pi$
$761$	−3.92491	+	6.79815i	−0.142278	+	0.246433i	0.786076	+	0.618130i	$0.212109\pi$
$762$		0			0
$763$	−30.3170	−	8.44244i	−1.09755	−	0.305637i
$764$	−27.7372	+	27.1269i	−1.00350	+	0.981419i
$765$		0			0
$766$	7.64613	−	9.85072i	0.276266	−	0.355921i
$767$	7.48280	+	12.9606i	0.270188	+	0.467980i
$768$		0			0
$769$	24.0398			0.866898			0.433449	−	0.901178i	$-0.357297\pi$
$769$	24.0398			0.866898			0.433449	+	0.901178i	$0.357297\pi$
$770$	0.814762	+	1.09627i	0.0293620	+	0.0395067i
$771$		0			0
$772$	−1.26898	−	4.95573i	−0.0456717	−	0.178361i
$773$	−16.6890	+	9.63541i	−0.600262	+	0.346562i	−0.769145	−	0.639075i	$-0.779318\pi$
$773$	−16.6890	+	9.63541i	−0.600262	+	0.346562i	0.168882	+	0.985636i	$0.445984\pi$
$774$		0			0
$775$	2.54970	−	4.41622i	0.0915881	−	0.158635i
$776$	−49.4162	−	21.4415i	−1.77394	−	0.769705i
$777$		0			0
$778$	−17.0419	+	6.94823i	−0.610983	+	0.249106i
$779$	37.1958	+	21.4750i	1.33268	+	0.769422i
$780$		0			0
$781$	−0.814031	+	0.469981i	−0.0291283	+	0.0168172i
$782$	−5.49414	−	0.754423i	−0.196470	−	0.0269781i
$783$		0			0
$784$	−15.0017	+	23.6421i	−0.535777	+	0.844360i
$785$	63.5378			2.26776
$786$		0			0
$787$	−36.8732	+	21.2888i	−1.31439	+	0.758863i	−0.982820	−	0.184568i	$-0.940911\pi$
$787$	−36.8732	+	21.2888i	−1.31439	+	0.758863i	−0.331569	+	0.943431i	$0.607578\pi$
$788$	2.06716	−	7.38520i	0.0736395	−	0.263087i
$789$		0			0
$790$	−6.97445	+	2.84358i	−0.248140	+	0.101170i
$791$	20.8863	+	21.2994i	0.742632	+	0.757321i
$792$		0			0
$793$	−1.53317	+	2.65552i	−0.0544443	+	0.0943003i
$794$	10.9528	+	8.50158i	0.388701	+	0.301710i
$795$		0			0
$796$	8.46643	+	33.0638i	0.300085	+	1.17191i
$797$		−	14.7345i		−	0.521923i	−0.965349	−	0.260962i	$-0.915960\pi$
$797$		−	14.7345i		−	0.521923i	0.965349	−	0.260962i	$-0.0840396\pi$
$798$		0			0
$799$	2.47014			0.0873873
$800$	−5.79839	+	36.2286i	−0.205004	+	1.28087i
$801$		0			0
$802$	−2.17892	+	2.80716i	−0.0769404	+	0.0991244i
$803$	0.818361	+	0.472481i	0.0288793	+	0.0166735i
$804$		0			0
$805$	78.8479	+	21.9570i	2.77902	+	0.773882i
$806$	−1.54476	+	0.629819i	−0.0544118	+	0.0221844i
$807$		0			0
$808$	−9.35764	+	1.07347i	−0.329201	+	0.0377647i
$809$	−6.93906	−	12.0188i	−0.243964	−	0.422558i	0.717876	−	0.696171i	$-0.245115\pi$
$809$	−6.93906	−	12.0188i	−0.243964	−	0.422558i	−0.961840	+	0.273613i	$0.911781\pi$
$810$		0			0
$811$		−	44.9188i		−	1.57731i	−0.614835	−	0.788656i	$-0.710777\pi$
$811$		−	44.9188i		−	1.57731i	0.614835	−	0.788656i	$-0.289223\pi$
$812$	−36.8836	+	20.2784i	−1.29436	+	0.711632i
$813$		0			0
$814$	−1.33988	−	0.183984i	−0.0469627	−	0.00644864i
$815$	4.33795	+	7.51355i	0.151952	+	0.263188i
$816$		0			0
$817$	−16.6218	+	28.7898i	−0.581524	+	1.00723i
$818$	−8.05329	−	19.7523i	−0.281577	−	0.690624i
$819$		0			0
$820$	−40.7306	−	41.6468i	−1.42237	−	1.45437i
$821$	−4.28623	−	2.47466i	−0.149591	−	0.0863661i	0.423336	−	0.905973i	$-0.360859\pi$
$821$	−4.28623	−	2.47466i	−0.149591	−	0.0863661i	−0.572927	+	0.819606i	$0.694192\pi$
$822$		0			0
$823$	−4.28025	−	7.41361i	−0.149200	−	0.258422i	0.781732	−	0.623615i	$-0.214337\pi$
$823$	−4.28025	−	7.41361i	−0.149200	−	0.258422i	−0.930932	+	0.365192i	$0.881003\pi$
$824$	29.6848	−	22.0010i	1.03412	−	0.766443i
$825$		0			0
$826$	34.2582	+	14.8104i	1.19200	+	0.515321i
$827$			8.43880i			0.293446i	0.989178	+	0.146723i	$0.0468726\pi$
$827$			8.43880i			0.293446i	−0.989178	+	0.146723i	$0.953127\pi$
$828$		0			0
$829$	35.8643	−	20.7062i	1.24562	−	0.719158i	0.275385	−	0.961334i	$-0.411195\pi$
$829$	35.8643	−	20.7062i	1.24562	−	0.719158i	0.970232	+	0.242176i	$0.0778613\pi$
$830$	3.91626	−	5.04542i	0.135935	−	0.175129i
$831$		0			0
$832$	8.76554	−	8.19930i	0.303890	−	0.284259i
$833$	−2.63326	+	1.45231i	−0.0912370	+	0.0503195i
$834$		0			0
$835$	−17.2800	−	9.97662i	−0.597999	−	0.345255i
$836$	1.03675	+	0.290192i	0.0358567	+	0.0100365i
$837$		0			0
$838$	3.51119	−	25.5705i	0.121292	−	0.883320i
$839$	33.1939			1.14598			0.572990	−	0.819563i	$-0.305783\pi$
$839$	33.1939			1.14598			0.572990	+	0.819563i	$0.305783\pi$
$840$		0			0
$841$	−34.2720			−1.18179
$842$	6.61101	−	48.1452i	0.227830	−	1.65919i
$843$		0			0
$844$	−6.93281	+	24.7684i	−0.238637	+	0.852563i
$845$	31.5487	+	18.2146i	1.08531	+	0.626603i
$846$		0			0
$847$	28.1543	−	7.24919i	0.967393	−	0.249085i
$848$	−1.32101	−	0.0293888i	−0.0453638	−	0.00100922i
$849$		0			0
$850$	−2.41615	+	3.11280i	−0.0828734	+	0.106768i
$851$	−70.1854	+	40.5216i	−2.40593	+	1.38906i
$852$		0			0
$853$		−	7.36144i		−	0.252051i	−0.992027	−	0.126025i	$-0.959778\pi$
$853$		−	7.36144i		−	0.252051i	0.992027	−	0.126025i	$-0.0402221\pi$
$854$	0.881629	+	7.59611i	0.0301687	+	0.259933i
$855$		0			0
$856$	−7.79607	−	10.5188i	−0.266464	−	0.359526i
$857$	−16.7624	−	29.0332i	−0.572591	−	0.991757i	−0.996299	−	0.0859578i	$-0.972605\pi$
$857$	−16.7624	−	29.0332i	−0.572591	−	0.991757i	0.423708	−	0.905799i	$-0.360728\pi$
$858$		0			0
$859$	−16.1210	−	9.30748i	−0.550043	−	0.317567i	0.199097	−	0.979980i	$-0.436199\pi$
$859$	−16.1210	−	9.30748i	−0.550043	−	0.317567i	−0.749139	+	0.662413i	$0.769533\pi$
$860$	32.2349	−	31.5258i	1.09920	−	1.07502i
$861$		0			0
$862$	13.6777	+	33.5474i	0.465865	+	1.14263i
$863$	−1.08784	+	1.88420i	−0.0370307	+	0.0641390i	−0.883947	−	0.467588i	$-0.845123\pi$
$863$	−1.08784	+	1.88420i	−0.0370307	+	0.0641390i	0.846916	+	0.531727i	$0.178457\pi$
$864$		0			0
$865$	12.8161	+	22.1981i	0.435759	+	0.754757i
$866$	5.31497	+	0.729820i	0.180610	+	0.0248003i
$867$		0			0
$868$	−2.15507	+	3.55868i	−0.0731478	+	0.120789i
$869$		−	0.169267i		−	0.00574199i
$870$		0			0
$871$	−2.41945	−	4.19060i	−0.0819798	−	0.141993i
$872$	33.4242	−	3.83430i	1.13189	−	0.129846i
$873$		0			0
$874$	59.7386	−	24.3562i	2.02069	−	0.823862i
$875$	9.51286	−	9.32835i	0.321593	−	0.315356i
$876$		0			0
$877$	−26.2726	−	15.1685i	−0.887161	−	0.512203i	−0.0141482	−	0.999900i	$-0.504504\pi$
$877$	−26.2726	−	15.1685i	−0.887161	−	0.512203i	−0.873013	+	0.487697i	$0.837837\pi$
$878$	−7.77030	+	10.0107i	−0.262235	+	0.337845i
$879$		0			0
$880$	−1.24801	−	0.758041i	−0.0420704	−	0.0255535i
$881$	−10.1482			−0.341902			−0.170951	−	0.985280i	$-0.554684\pi$
$881$	−10.1482			−0.341902			−0.170951	+	0.985280i	$0.554684\pi$
$882$		0			0
$883$			16.3012i			0.548578i	0.961647	+	0.274289i	$0.0884424\pi$
$883$			16.3012i			0.548578i	−0.961647	+	0.274289i	$0.911558\pi$
$884$	1.24879	−	0.319771i	0.0420014	−	0.0107550i
$885$		0			0
$886$	14.8776	+	11.5480i	0.499823	+	0.387963i
$887$	6.02108	−	10.4288i	0.202168	−	0.350165i	−0.747059	−	0.664758i	$-0.768535\pi$
$887$	6.02108	−	10.4288i	0.202168	−	0.350165i	0.949227	+	0.314593i	$0.101868\pi$
$888$		0			0
$889$	15.0451	+	15.3427i	0.504596	+	0.514576i
$890$	−32.1683	+	13.1154i	−1.07828	+	0.439630i
$891$		0			0
$892$	23.3278	+	6.52957i	0.781071	+	0.218626i
$893$	−24.8853	+	14.3676i	−0.832756	+	0.480792i
$894$		0			0
$895$	38.1992			1.27686
$896$	5.34770	−	29.4517i	0.178654	−	0.983912i
$897$		0			0
$898$	−37.5325	−	5.15374i	−1.25248	−	0.171983i
$899$	−5.41611	+	3.12699i	−0.180637	+	0.104291i
$900$		0			0
$901$	−0.122899	−	0.0709560i	−0.00409437	−	0.00236389i
$902$	1.21227	−	0.494258i	0.0403641	−	0.0164570i
$903$		0			0
$904$	−29.2557	−	12.6940i	−0.973031	−	0.422195i
$905$	−23.2657	+	40.2974i	−0.773379	+	1.33953i
$906$		0			0
$907$	−31.2195	+	18.0246i	−1.03663	+	0.598496i	−0.918876	−	0.394547i	$-0.870902\pi$
$907$	−31.2195	+	18.0246i	−1.03663	+	0.598496i	−0.117750	+	0.993043i	$0.537568\pi$
$908$	13.4397	−	3.44141i	0.446011	−	0.114207i
$909$		0			0
$910$	−18.8985	+	2.19342i	−0.626479	+	0.0727112i
$911$	36.9774			1.22512			0.612558	−	0.790426i	$-0.290141\pi$
$911$	36.9774			1.22512			0.612558	+	0.790426i	$0.290141\pi$
$912$		0			0
$913$	0.0717687	+	0.124307i	0.00237520	+	0.00411396i
$914$	−11.8617	+	15.2818i	−0.392351	+	0.505476i
$915$		0			0
$916$	12.2778	+	12.5540i	0.405670	+	0.414796i
$917$	−7.41306	−	28.7907i	−0.244801	−	0.950754i
$918$		0			0
$919$	4.10501	−	7.11009i	0.135412	−	0.234540i	−0.790343	−	0.612665i	$-0.790098\pi$
$919$	4.10501	−	7.11009i	0.135412	−	0.234540i	0.925755	+	0.378125i	$0.123431\pi$
$920$	−86.9291	+	9.97219i	−2.86597	+	0.328773i
$921$		0			0
$922$	−5.40741	+	39.3799i	−0.178084	+	1.29691i
$923$		−	13.0927i		−	0.430952i
$924$		0			0
$925$			57.5848i			1.89338i
$926$	0.572417	+	0.0786008i	0.0188108	+	0.00258298i
$927$		0			0
$928$	28.3741	−	34.9230i	0.931426	−	1.14640i
$929$	−12.0428	+	20.8588i	−0.395112	+	0.684355i	−0.993116	−	0.117139i	$-0.962628\pi$
$929$	−12.0428	+	20.8588i	−0.395112	+	0.684355i	0.598003	+	0.801494i	$0.295961\pi$
$930$		0			0
$931$	18.0813	−	29.9476i	0.592591	−	0.981492i
$932$	23.4635	−	22.9473i	0.768572	−	0.751664i
$933$		0			0
$934$	18.8954	+	14.6666i	0.618275	+	0.479905i
$935$	−0.0784123	−	0.135814i	−0.00256435	−	0.00444159i
$936$		0			0
$937$	25.0333			0.817802			0.408901	−	0.912579i	$-0.365912\pi$
$937$	25.0333			0.817802			0.408901	+	0.912579i	$0.365912\pi$
$938$	−11.0769	−	4.78872i	−0.361672	−	0.156357i
$939$		0			0
$940$	37.7554	−	9.66779i	1.23144	−	0.315328i
$941$	12.5109	−	7.22317i	0.407844	−	0.235469i	−0.282019	−	0.959409i	$-0.591004\pi$
$941$	12.5109	−	7.22317i	0.407844	−	0.235469i	0.689863	+	0.723940i	$0.257671\pi$
$942$		0			0
$943$	39.2243	−	67.9384i	1.27732	−	2.21238i
$944$	−39.8897	−	0.887432i	−1.29830	−	0.0288835i
$945$		0			0
$946$	0.382559	+	0.938303i	0.0124381	+	0.0305069i
$947$	5.53236	+	3.19411i	0.179777	+	0.103795i	0.587188	−	0.809450i	$-0.300235\pi$
$947$	5.53236	+	3.19411i	0.179777	+	0.103795i	−0.407411	+	0.913245i	$0.633568\pi$
$948$		0			0
$949$	−11.3989	+	6.58117i	−0.370025	+	0.213634i
$950$	6.23588	−	45.4133i	0.202319	−	1.47340i
$951$		0			0
$952$	2.02390	−	2.49780i	0.0655949	−	0.0809541i
$953$	−18.8800			−0.611583			−0.305791	−	0.952099i	$-0.598921\pi$
$953$	−18.8800			−0.611583			−0.305791	+	0.952099i	$0.598921\pi$
$954$		0			0
$955$	−56.9355	+	32.8717i	−1.84239	+	1.06370i
$956$	1.57238	+	0.440118i	0.0508544	+	0.0142344i
$957$		0			0
$958$	−10.4292	−	25.5797i	−0.336952	−	0.826443i
$959$	4.57067	−	16.4134i	0.147595	−	0.530015i
$960$		0			0
$961$	15.1909	−	26.3114i	0.490030	−	0.848756i
$962$	11.5509	−	14.8814i	0.372417	−	0.479795i
$963$		0			0
$964$	11.9370	+	46.6171i	0.384463	+	1.50144i
$965$		−	8.66864i		−	0.279053i
$966$		0			0
$967$	−23.9119			−0.768954			−0.384477	−	0.923135i	$-0.625618\pi$
$967$	−23.9119			−0.768954			−0.384477	+	0.923135i	$0.625618\pi$
$968$	−24.9695	+	18.5063i	−0.802551	+	0.594814i
$969$		0			0
$970$	−72.1076	−	55.9699i	−2.31524	−	1.79709i
$971$	−29.6865	−	17.1395i	−0.952685	−	0.550033i	−0.0587710	−	0.998271i	$-0.518718\pi$
$971$	−29.6865	−	17.1395i	−0.952685	−	0.550033i	−0.893914	+	0.448239i	$0.852052\pi$
$972$		0			0
$973$	−21.1838	+	20.7729i	−0.679121	+	0.665949i
$974$	−19.0403	−	46.7001i	−0.610089	−	1.49637i
$975$		0			0
$976$	−3.92907	−	7.16900i	−0.125766	−	0.229474i
$977$	−1.82067	−	3.15350i	−0.0582485	−	0.100889i	0.835431	−	0.549596i	$-0.185218\pi$
$977$	−1.82067	−	3.15350i	−0.0582485	−	0.100889i	−0.893679	+	0.448706i	$0.851885\pi$
$978$		0			0
$979$		−	0.780710i		−	0.0249516i
$980$	−34.5644	+	32.5043i	−1.10412	+	1.03831i
$981$		0			0
$982$	−3.73047	+	27.1674i	−0.119044	+	0.866947i
$983$	22.4101	+	38.8154i	0.714771	+	1.23802i	0.963048	+	0.269331i	$0.0868025\pi$
$983$	22.4101	+	38.8154i	0.714771	+	1.23802i	−0.248277	+	0.968689i	$0.579864\pi$
$984$		0			0
$985$	6.49776	−	11.2544i	0.207036	−	0.358597i
$986$	4.47500	−	1.82452i	0.142513	−	0.0581045i
$987$		0			0
$988$	−10.7210	+	10.4851i	−0.341079	+	0.333576i
$989$	52.5848	+	30.3599i	1.67210	+	0.965388i
$990$		0			0
$991$	−23.9629	−	41.5050i	−0.761208	−	1.31845i	−0.942228	−	0.334972i	$-0.891273\pi$
$991$	−23.9629	−	41.5050i	−0.761208	−	1.31845i	0.181020	−	0.983479i	$-0.442060\pi$
$992$	0.702894	−	4.39171i	0.0223169	−	0.139437i
$993$		0			0
$994$	−19.4771	−	26.2065i	−0.617776	−	0.831220i
$995$			57.8356i			1.83351i
$996$		0			0
$997$	−38.4617	+	22.2059i	−1.21810	+	0.703268i	−0.964510	−	0.264045i	$-0.914943\pi$
$997$	−38.4617	+	22.2059i	−1.21810	+	0.703268i	−0.253585	+	0.967313i	$0.581610\pi$
$998$	−14.8080	−	11.4940i	−0.468738	−	0.363835i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.16		32
3.2	odd	2		168.2.bc.a.37.1	✓	32
4.3	odd	2		2016.2.cr.e.1297.14		32
7.4	even	3	inner	504.2.cj.e.109.6		32
8.3	odd	2		2016.2.cr.e.1297.3		32
8.5	even	2	inner	504.2.cj.e.37.6		32
12.11	even	2		672.2.bk.a.625.2		32
21.2	odd	6		1176.2.c.e.589.12		16
21.5	even	6		1176.2.c.f.589.12		16
21.11	odd	6		168.2.bc.a.109.11	yes	32
24.5	odd	2		168.2.bc.a.37.11	yes	32
24.11	even	2		672.2.bk.a.625.15		32
28.11	odd	6		2016.2.cr.e.1873.3		32
56.11	odd	6		2016.2.cr.e.1873.14		32
56.53	even	6	inner	504.2.cj.e.109.16		32
84.11	even	6		672.2.bk.a.529.15		32
84.23	even	6		4704.2.c.e.2353.7		16
84.47	odd	6		4704.2.c.f.2353.10		16
168.5	even	6		1176.2.c.f.589.11		16
168.11	even	6		672.2.bk.a.529.2		32
168.53	odd	6		168.2.bc.a.109.1	yes	32
168.107	even	6		4704.2.c.e.2353.10		16
168.131	odd	6		4704.2.c.f.2353.7		16
168.149	odd	6		1176.2.c.e.589.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.1	✓	32	3.2	odd	2
168.2.bc.a.37.11	yes	32	24.5	odd	2
168.2.bc.a.109.1	yes	32	168.53	odd	6
168.2.bc.a.109.11	yes	32	21.11	odd	6
504.2.cj.e.37.6		32	8.5	even	2	inner
504.2.cj.e.37.16		32	1.1	even	1	trivial
504.2.cj.e.109.6		32	7.4	even	3	inner
504.2.cj.e.109.16		32	56.53	even	6	inner
672.2.bk.a.529.2		32	168.11	even	6
672.2.bk.a.529.15		32	84.11	even	6
672.2.bk.a.625.2		32	12.11	even	2
672.2.bk.a.625.15		32	24.11	even	2
1176.2.c.e.589.11		16	168.149	odd	6
1176.2.c.e.589.12		16	21.2	odd	6
1176.2.c.f.589.11		16	168.5	even	6
1176.2.c.f.589.12		16	21.5	even	6
2016.2.cr.e.1297.3		32	8.3	odd	2
2016.2.cr.e.1297.14		32	4.3	odd	2
2016.2.cr.e.1873.3		32	28.11	odd	6
2016.2.cr.e.1873.14		32	56.11	odd	6
4704.2.c.e.2353.7		16	84.23	even	6
4704.2.c.e.2353.10		16	168.107	even	6
4704.2.c.f.2353.7		16	168.131	odd	6
4704.2.c.f.2353.10		16	84.47	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)

\(f(q)\)	\(=\)	\(q+(1.40107 + 0.192386i) q^{2} +(1.92598 + 0.539091i) q^{4} +(2.93503 + 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 + 1.12583i) q^{8} +O(q^{10})\)	\(q+(1.40107 + 0.192386i) q^{2} +(1.92598 + 0.539091i) q^{4} +(2.93503 + 1.69454i) q^{5} +(-1.85242 - 1.88906i) q^{7} +(2.59471 + 1.12583i) q^{8} +(3.78617 + 2.93882i) q^{10} +(-0.0932820 + 0.0538564i) q^{11} -1.50033i q^{13} +(-2.23193 - 3.00308i) q^{14} +(3.41876 + 2.07655i) q^{16} +(0.214800 + 0.372045i) q^{17} +(-4.32799 - 2.49877i) q^{19} +(4.73929 + 4.84589i) q^{20} +(-0.141056 + 0.0575103i) q^{22} +(-4.56401 + 7.90510i) q^{23} +(3.24294 + 5.61694i) q^{25} +(0.288642 - 2.10206i) q^{26} +(-2.54934 - 4.63690i) q^{28} -7.95437i q^{29} +(-0.393116 - 0.680897i) q^{31} +(4.39041 + 3.56711i) q^{32} +(0.229373 + 0.562584i) q^{34} +(-2.23582 - 8.68345i) q^{35} +(7.68900 + 4.43925i) q^{37} +(-5.58307 - 4.33358i) q^{38} +(5.70777 + 7.70119i) q^{40} -8.59425 q^{41} -6.65201i q^{43} +(-0.208692 + 0.0534386i) q^{44} +(-7.91532 + 10.1975i) q^{46} +(2.87493 - 4.97953i) q^{47} +(-0.137086 + 6.99866i) q^{49} +(3.46295 + 8.49360i) q^{50} +(0.808814 - 2.88960i) q^{52} +(-0.286078 + 0.165167i) q^{53} -0.365048 q^{55} +(-2.67972 - 6.98707i) q^{56} +(1.53031 - 11.1446i) q^{58} +(-8.63850 + 4.98744i) q^{59} +(-1.76996 - 1.02189i) q^{61} +(-0.419787 - 1.02961i) q^{62} +(5.46500 + 5.84241i) q^{64} +(2.54237 - 4.40351i) q^{65} +(2.79312 - 1.61261i) q^{67} +(0.213134 + 0.832346i) q^{68} +(-1.46196 - 12.5962i) q^{70} +8.72656 q^{71} +(-4.38649 - 7.59762i) q^{73} +(9.91876 + 7.69894i) q^{74} +(-6.98854 - 7.14574i) q^{76} +(0.274535 + 0.0764506i) q^{77} +(-0.785733 + 1.36093i) q^{79} +(6.51537 + 11.8880i) q^{80} +(-12.0411 - 1.65341i) q^{82} -1.33259i q^{83} +1.45595i q^{85} +(1.27975 - 9.31991i) q^{86} +(-0.302673 + 0.0347215i) q^{88} +(-3.62404 + 6.27701i) q^{89} +(-2.83421 + 2.77924i) q^{91} +(-13.0517 + 12.7646i) q^{92} +(4.98596 - 6.42355i) q^{94} +(-8.46852 - 14.6679i) q^{95} -19.0450 q^{97} +(-1.53851 + 9.77921i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 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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