LMFDB - Embedded newform 504.2.cj.e.37.11

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			37.11
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.e.109.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.446345 - 1.34193i) q^{2} +(-1.60155 - 1.19793i) q^{4} +(1.98722 + 1.14732i) q^{5} +(-1.05630 - 2.42574i) q^{7} +(-2.32238 + 1.61448i) q^{8} +O(q^{10})$	\(q+(0.446345 - 1.34193i) q^{2} +(-1.60155 - 1.19793i) q^{4} +(1.98722 + 1.14732i) q^{5} +(-1.05630 - 2.42574i) q^{7} +(-2.32238 + 1.61448i) q^{8} +(2.42662 - 2.15461i) q^{10} +(3.36596 - 1.94334i) q^{11} -3.33413i q^{13} +(-3.72665 + 0.334768i) q^{14} +(1.12994 + 3.83709i) q^{16} +(0.143560 + 0.248654i) q^{17} +(-2.41210 - 1.39263i) q^{19} +(-1.80823 - 4.21805i) q^{20} +(-1.10544 - 5.38428i) q^{22} +(3.26713 - 5.65883i) q^{23} +(0.132707 + 0.229856i) q^{25} +(-4.47417 - 1.48817i) q^{26} +(-1.21414 + 5.15033i) q^{28} +5.53374i q^{29} +(-3.72154 - 6.44589i) q^{31} +(5.65345 + 0.196361i) q^{32} +(0.397754 - 0.0816627i) q^{34} +(0.684001 - 6.03242i) q^{35} +(5.15752 + 2.97769i) q^{37} +(-2.94544 + 2.61528i) q^{38} +(-6.46742 + 0.543818i) q^{40} +3.51617 q^{41} +11.2465i q^{43} +(-7.71873 - 0.919816i) q^{44} +(-6.13549 - 6.91004i) q^{46} +(0.0435037 - 0.0753507i) q^{47} +(-4.76845 + 5.12464i) q^{49} +(0.367684 - 0.0754890i) q^{50} +(-3.99404 + 5.33978i) q^{52} +(-6.11258 + 3.52910i) q^{53} +8.91855 q^{55} +(6.36946 + 3.92811i) q^{56} +(7.42590 + 2.46996i) q^{58} +(-3.76909 + 2.17609i) q^{59} +(-6.20693 - 3.58357i) q^{61} +(-10.3110 + 2.11695i) q^{62} +(2.78689 - 7.49888i) q^{64} +(3.82533 - 6.62566i) q^{65} +(11.2804 - 6.51276i) q^{67} +(0.0679497 - 0.570207i) q^{68} +(-7.78978 - 3.61042i) q^{70} +6.18835 q^{71} +(6.93978 + 12.0201i) q^{73} +(6.29789 - 5.59195i) q^{74} +(2.19484 + 5.11989i) q^{76} +(-8.26950 - 6.11219i) q^{77} +(4.49926 - 7.79295i) q^{79} +(-2.15694 + 8.92156i) q^{80} +(1.56942 - 4.71846i) q^{82} +17.6313i q^{83} +0.658842i q^{85} +(15.0921 + 5.01983i) q^{86} +(-4.67954 + 9.94744i) q^{88} +(-8.59194 + 14.8817i) q^{89} +(-8.08774 + 3.52185i) q^{91} +(-12.0113 + 5.14913i) q^{92} +(-0.0816977 - 0.0920113i) q^{94} +(-3.19559 - 5.53493i) q^{95} +6.46528 q^{97} +(4.74854 + 8.68628i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.446345	−	1.34193i	0.315613	−	0.948888i
$2$	0.446345	−	1.34193i	0.315613	−	0.948888i
$3$		0			0
$3$		0			0
$4$	−1.60155	−	1.19793i	−0.800776	−	0.598964i
$5$	1.98722	+	1.14732i	0.888714	+	0.513099i	0.873522	−	0.486785i	$-0.161831\pi$
$5$	1.98722	+	1.14732i	0.888714	+	0.513099i	0.0151922	+	0.999885i	$0.495164\pi$
$6$		0			0
$7$	−1.05630	−	2.42574i	−0.399245	−	0.916844i
$7$	−1.05630	−	2.42574i	−0.399245	−	0.916844i
$8$	−2.32238	+	1.61448i	−0.821085	+	0.570806i
$9$		0			0
$10$	2.42662	−	2.15461i	0.767364	−	0.681349i
$11$	3.36596	−	1.94334i	1.01487	−	0.585938i	0.102259	−	0.994758i	$-0.467393\pi$
$11$	3.36596	−	1.94334i	1.01487	−	0.585938i	0.912615	+	0.408820i	$0.134060\pi$
$12$		0			0
$13$		−	3.33413i		−	0.924721i	−0.886692	−	0.462361i	$-0.847003\pi$
$13$		−	3.33413i		−	0.924721i	0.886692	−	0.462361i	$-0.152997\pi$
$14$	−3.72665	+	0.334768i	−0.995989	+	0.0894705i
$15$		0			0
$16$	1.12994	+	3.83709i	0.282485	+	0.959272i
$17$	0.143560	+	0.248654i	0.0348185	+	0.0603074i	0.882910	−	0.469543i	$-0.155581\pi$
$17$	0.143560	+	0.248654i	0.0348185	+	0.0603074i	−0.848091	+	0.529851i	$0.822248\pi$
$18$		0			0
$19$	−2.41210	−	1.39263i	−0.553374	−	0.319491i	0.197108	−	0.980382i	$-0.436845\pi$
$19$	−2.41210	−	1.39263i	−0.553374	−	0.319491i	−0.750482	+	0.660891i	$0.770178\pi$
$20$	−1.80823	−	4.21805i	−0.404333	−	0.943185i
$21$		0			0
$22$	−1.10544	−	5.38428i	−0.235681	−	1.14793i
$23$	3.26713	−	5.65883i	0.681243	−	1.17995i	−0.293359	−	0.956002i	$-0.594773\pi$
$23$	3.26713	−	5.65883i	0.681243	−	1.17995i	0.974602	−	0.223945i	$-0.0718935\pi$
$24$		0			0
$25$	0.132707	+	0.229856i	0.0265415	+	0.0459712i
$26$	−4.47417	−	1.48817i	−0.877457	−	0.291854i
$27$		0			0
$28$	−1.21414	+	5.15033i	−0.229450	+	0.973320i
$29$			5.53374i			1.02759i	0.857913	+	0.513795i	$0.171761\pi$
$29$			5.53374i			1.02759i	−0.857913	+	0.513795i	$0.828239\pi$
$30$		0			0
$31$	−3.72154	−	6.44589i	−0.668408	−	1.15772i	−0.978349	−	0.206961i	$-0.933643\pi$
$31$	−3.72154	−	6.44589i	−0.668408	−	1.15772i	0.309941	−	0.950756i	$-0.399691\pi$
$32$	5.65345	+	0.196361i	0.999397	+	0.0347121i
$33$		0			0
$34$	0.397754	−	0.0816627i	0.0682142	−	0.0140050i
$35$	0.684001	−	6.03242i	0.115617	−	1.01966i
$36$		0			0
$37$	5.15752	+	2.97769i	0.847890	+	0.489530i	0.859939	−	0.510398i	$-0.170502\pi$
$37$	5.15752	+	2.97769i	0.847890	+	0.489530i	−0.0120481	+	0.999927i	$0.503835\pi$
$38$	−2.94544	+	2.61528i	−0.477813	+	0.424254i
$39$		0			0
$40$	−6.46742	+	0.543818i	−1.02259	+	0.0859851i
$41$	3.51617			0.549134			0.274567	−	0.961568i	$-0.411466\pi$
$41$	3.51617			0.549134			0.274567	+	0.961568i	$0.411466\pi$
$42$		0			0
$43$			11.2465i			1.71508i	0.514416	+	0.857541i	$0.328009\pi$
$43$			11.2465i			1.71508i	−0.514416	+	0.857541i	$0.671991\pi$
$44$	−7.71873	−	0.919816i	−1.16364	−	0.138667i
$45$		0			0
$46$	−6.13549	−	6.91004i	−0.904628	−	1.01883i
$47$	0.0435037	−	0.0753507i	0.00634567	−	0.0109910i	−0.862835	−	0.505485i	$-0.831313\pi$
$47$	0.0435037	−	0.0753507i	0.00634567	−	0.0109910i	0.869181	+	0.494494i	$0.164647\pi$
$48$		0			0
$49$	−4.76845	+	5.12464i	−0.681207	+	0.732091i
$50$	0.367684	−	0.0754890i	0.0519983	−	0.0106758i
$51$		0			0
$52$	−3.99404	+	5.33978i	−0.553874	+	0.740495i
$53$	−6.11258	+	3.52910i	−0.839627	+	0.484759i	−0.857137	−	0.515088i	$-0.827759\pi$
$53$	−6.11258	+	3.52910i	−0.839627	+	0.484759i	0.0175103	+	0.999847i	$0.494426\pi$
$54$		0			0
$55$	8.91855			1.20258
$56$	6.36946	+	3.92811i	0.851154	+	0.524915i
$57$		0			0
$58$	7.42590	+	2.46996i	0.975068	+	0.324321i
$59$	−3.76909	+	2.17609i	−0.490694	+	0.283302i	−0.724862	−	0.688894i	$-0.758097\pi$
$59$	−3.76909	+	2.17609i	−0.490694	+	0.283302i	0.234168	+	0.972196i	$0.424763\pi$
$60$		0			0
$61$	−6.20693	−	3.58357i	−0.794716	−	0.458829i	0.0469043	−	0.998899i	$-0.485064\pi$
$61$	−6.20693	−	3.58357i	−0.794716	−	0.458829i	−0.841620	+	0.540070i	$0.818398\pi$
$62$	−10.3110	+	2.11695i	−1.30950	+	0.268853i
$63$		0			0
$64$	2.78689	−	7.49888i	0.348361	−	0.937360i
$65$	3.82533	−	6.62566i	0.474474	−	0.821812i
$66$		0			0
$67$	11.2804	−	6.51276i	1.37812	−	0.795661i	0.386191	−	0.922419i	$-0.373791\pi$
$67$	11.2804	−	6.51276i	1.37812	−	0.795661i	0.991934	+	0.126758i	$0.0404573\pi$
$68$	0.0679497	−	0.570207i	0.00824011	−	0.0691478i
$69$		0			0
$70$	−7.78978	−	3.61042i	−0.931057	−	0.431528i
$71$	6.18835			0.734421			0.367211	−	0.930138i	$-0.380313\pi$
$71$	6.18835			0.734421			0.367211	+	0.930138i	$0.380313\pi$
$72$		0			0
$73$	6.93978	+	12.0201i	0.812240	+	1.40684i	0.911293	+	0.411759i	$0.135085\pi$
$73$	6.93978	+	12.0201i	0.812240	+	1.40684i	−0.0990526	+	0.995082i	$0.531581\pi$
$74$	6.29789	−	5.59195i	0.732114	−	0.650051i
$75$		0			0
$76$	2.19484	+	5.11989i	0.251766	+	0.587291i
$77$	−8.26950	−	6.11219i	−0.942397	−	0.696549i
$78$		0			0
$79$	4.49926	−	7.79295i	0.506207	−	0.876776i	−0.493767	−	0.869594i	$-0.664381\pi$
$79$	4.49926	−	7.79295i	0.506207	−	0.876776i	0.999974	−	0.00718179i	$-0.00228606\pi$
$80$	−2.15694	+	8.92156i	−0.241153	+	0.997461i
$81$		0			0
$82$	1.56942	−	4.71846i	0.173314	−	0.521066i
$83$			17.6313i			1.93529i	0.252312	+	0.967646i	$0.418809\pi$
$83$			17.6313i			1.93529i	−0.252312	+	0.967646i	$0.581191\pi$
$84$		0			0
$85$			0.658842i			0.0714614i
$86$	15.0921	+	5.01983i	1.62742	+	0.541303i
$87$		0			0
$88$	−4.67954	+	9.94744i	−0.498841	+	1.06040i
$89$	−8.59194	+	14.8817i	−0.910744	+	1.57745i	−0.0977280	+	0.995213i	$0.531158\pi$
$89$	−8.59194	+	14.8817i	−0.910744	+	1.57745i	−0.813016	+	0.582242i	$0.802176\pi$
$90$		0			0
$91$	−8.08774	+	3.52185i	−0.847825	+	0.369190i
$92$	−12.0113	+	5.14913i	−1.25227	+	0.536834i
$93$		0			0
$94$	−0.0816977	−	0.0920113i	−0.00842647	−	0.00949025i
$95$	−3.19559	−	5.53493i	−0.327861	−	0.567871i
$96$		0			0
$97$	6.46528			0.656450			0.328225	−	0.944600i	$-0.393550\pi$
$97$	6.46528			0.656450			0.328225	+	0.944600i	$0.393550\pi$
$98$	4.74854	+	8.68628i	0.479674	+	0.877447i
$99$		0			0
$100$	0.0628127	−	0.527100i	0.00628127	−	0.0527100i
$101$	10.2590	−	5.92305i	1.02081	−	0.589365i	0.106472	−	0.994316i	$-0.466045\pi$
$101$	10.2590	−	5.92305i	1.02081	−	0.589365i	0.914339	+	0.404951i	$0.132711\pi$
$102$		0			0
$103$	−0.810948	+	1.40460i	−0.0799051	+	0.138400i	−0.903209	−	0.429201i	$-0.858795\pi$
$103$	−0.810948	+	1.40460i	−0.0799051	+	0.138400i	0.823304	+	0.567601i	$0.192128\pi$
$104$	5.38290	+	7.74311i	0.527836	+	0.759275i
$105$		0			0
$106$	2.00749	+	9.77785i	0.194984	+	0.949708i
$107$	4.35546	+	2.51463i	0.421059	+	0.243098i	0.695530	−	0.718497i	$-0.255170\pi$
$107$	4.35546	+	2.51463i	0.421059	+	0.243098i	−0.274471	+	0.961595i	$0.588503\pi$
$108$		0			0
$109$	0.177033	−	0.102210i	0.0169567	−	0.00978994i	−0.491498	−	0.870879i	$-0.663550\pi$
$109$	0.177033	−	0.102210i	0.0169567	−	0.00978994i	0.508454	+	0.861089i	$0.330217\pi$
$110$	3.98075	−	11.9681i	0.379549	−	1.14111i
$111$		0			0
$112$	8.11422	−	6.79407i	0.766722	−	0.641980i
$113$	14.9203			1.40358			0.701792	−	0.712382i	$-0.252384\pi$
$113$	14.9203			1.40358			0.701792	+	0.712382i	$0.252384\pi$
$114$		0			0
$115$	12.9850	−	7.49691i	1.21086	−	0.699090i
$116$	6.62902	−	8.86258i	0.615489	−	0.822870i
$117$		0			0
$118$	1.23784	+	6.02915i	0.113953	+	0.555028i
$119$	0.451527	−	0.610895i	0.0413914	−	0.0560006i
$120$		0			0
$121$	2.05311	−	3.55609i	0.186646	−	0.323281i
$122$	−7.57933	+	6.72976i	−0.686201	+	0.609283i
$123$		0			0
$124$	−1.76147	+	14.7816i	−0.158185	+	1.32742i
$125$		−	10.8642i		−	0.971725i
$126$		0			0
$127$	−6.29267			−0.558384			−0.279192	−	0.960235i	$-0.590067\pi$
$127$	−6.29267			−0.558384			−0.279192	+	0.960235i	$0.590067\pi$
$128$	−8.81906	−	7.08690i	−0.779502	−	0.626399i
$129$		0			0
$130$	−7.18376	−	8.09065i	−0.630058	−	0.709597i
$131$	1.07470	+	0.620480i	0.0938973	+	0.0542116i	0.546213	−	0.837646i	$-0.316069\pi$
$131$	1.07470	+	0.620480i	0.0938973	+	0.0542116i	−0.452316	+	0.891858i	$0.649402\pi$
$132$		0			0
$133$	−0.830243	+	7.32217i	−0.0719912	+	0.634913i
$134$	−3.70471	−	18.0445i	−0.320038	−	1.55881i
$135$		0			0
$136$	−0.734849	−	0.345693i	−0.0630128	−	0.0296429i
$137$	0.795096	+	1.37715i	0.0679296	+	0.117658i	0.897990	−	0.440016i	$-0.145027\pi$
$137$	0.795096	+	1.37715i	0.0679296	+	0.117658i	−0.830060	+	0.557674i	$0.811694\pi$
$138$		0			0
$139$		−	1.02981i		−	0.0873470i	−0.999046	−	0.0436735i	$-0.986094\pi$
$139$		−	1.02981i		−	0.0873470i	0.999046	−	0.0436735i	$-0.0139061\pi$
$140$	−8.32186	+	8.84185i	−0.703325	+	0.747273i
$141$		0			0
$142$	2.76214	−	8.30433i	0.231793	−	0.696884i
$143$	−6.47933	−	11.2225i	−0.541829	−	0.938476i
$144$		0			0
$145$	−6.34900	+	10.9968i	−0.527256	+	0.913234i
$146$	19.2276	−	3.94761i	1.59129	−	0.326707i
$147$		0			0
$148$	−4.69297	−	10.9473i	−0.385760	−	0.899859i
$149$	8.30672	+	4.79589i	0.680513	+	0.392895i	0.800048	−	0.599935i	$-0.204807\pi$
$149$	8.30672	+	4.79589i	0.680513	+	0.392895i	−0.119535	+	0.992830i	$0.538140\pi$
$150$		0			0
$151$	−3.49611	−	6.05544i	−0.284510	−	0.492785i	0.687981	−	0.725729i	$-0.258497\pi$
$151$	−3.49611	−	6.05544i	−0.284510	−	0.492785i	−0.972490	+	0.232944i	$0.925164\pi$
$152$	7.85019	−	0.660088i	0.636734	−	0.0535402i
$153$		0			0
$154$	−11.8932	+	8.36895i	−0.958380	+	0.674389i
$155$		−	17.0792i		−	1.37184i
$156$		0			0
$157$	−15.0324	+	8.67895i	−1.19971	+	0.692655i	−0.960492	−	0.278309i	$-0.910226\pi$
$157$	−15.0324	+	8.67895i	−1.19971	+	0.692655i	−0.239223	+	0.970965i	$0.576893\pi$
$158$	−8.44938	−	9.51604i	−0.672196	−	0.757056i
$159$		0			0
$160$	11.0094	+	6.87655i	0.870367	+	0.543639i
$161$	−17.1779	−	1.94776i	−1.35381	−	0.153505i
$162$		0			0
$163$	−13.6156	−	7.86099i	−1.06646	−	0.615720i	−0.139247	−	0.990258i	$-0.544468\pi$
$163$	−13.6156	−	7.86099i	−1.06646	−	0.615720i	−0.927212	+	0.374537i	$0.877802\pi$
$164$	−5.63133	−	4.21212i	−0.439733	−	0.328911i
$165$		0			0
$166$	23.6600	+	7.86966i	1.83637	+	0.610804i
$167$	0.102064			0.00789795			0.00394897	−	0.999992i	$-0.498743\pi$
$167$	0.102064			0.00789795			0.00394897	+	0.999992i	$0.498743\pi$
$168$		0			0
$169$	1.88358			0.144891
$170$	0.884119	+	0.294071i	0.0678089	+	0.0225542i
$171$		0			0
$172$	13.4725	−	18.0119i	1.02727	−	1.37340i
$173$	1.98126	+	1.14388i	0.150633	+	0.0869678i	0.573422	−	0.819260i	$-0.305616\pi$
$173$	1.98126	+	1.14388i	0.150633	+	0.0869678i	−0.422789	+	0.906228i	$0.638949\pi$
$174$		0			0
$175$	0.417392	−	0.564711i	0.0315518	−	0.0426881i
$176$	11.2601	+	10.7196i	0.848761	+	0.808021i
$177$		0			0
$178$	16.1352	+	18.1721i	1.20938	+	1.36206i
$179$	−16.1281	+	9.31154i	−1.20547	+	0.695978i	−0.961766	−	0.273873i	$-0.911695\pi$
$179$	−16.1281	+	9.31154i	−1.20547	+	0.695978i	−0.243702	+	0.969850i	$0.578362\pi$
$180$		0			0
$181$			13.6786i			1.01672i	0.861144	+	0.508361i	$0.169748\pi$
$181$			13.6786i			1.01672i	−0.861144	+	0.508361i	$0.830252\pi$
$182$	1.11616	+	12.4251i	0.0827353	+	0.921012i
$183$		0			0
$184$	1.54858	+	18.4167i	0.114163	+	1.35769i
$185$	6.83276	+	11.8347i	0.502355	+	0.870104i
$186$		0			0
$187$	0.966437	+	0.557972i	0.0706728	+	0.0408030i
$188$	−0.159938	+	0.0685638i	−0.0116647	+	0.00500053i
$189$		0			0
$190$	−8.85382	+	1.81777i	−0.642323	+	0.131875i
$191$	−6.31729	+	10.9419i	−0.457103	+	0.791726i	−0.998806	−	0.0488436i	$-0.984446\pi$
$191$	−6.31729	+	10.9419i	−0.457103	+	0.791726i	0.541703	+	0.840570i	$0.317780\pi$
$192$		0			0
$193$	−1.30291	−	2.25671i	−0.0937856	−	0.162441i	0.815316	−	0.579017i	$-0.196563\pi$
$193$	−1.30291	−	2.25671i	−0.0937856	−	0.162441i	−0.909101	+	0.416576i	$0.863230\pi$
$194$	2.88574	−	8.67595i	0.207184	−	0.622897i
$195$		0			0
$196$	13.7759	−	2.49513i	0.983990	−	0.178223i
$197$			0.794777i			0.0566255i	0.999599	+	0.0283127i	$0.00901343\pi$
$197$			0.794777i			0.0566255i	−0.999599	+	0.0283127i	$0.990987\pi$
$198$		0			0
$199$	−5.36714	−	9.29616i	−0.380466	−	0.658987i	0.610663	−	0.791891i	$-0.290903\pi$
$199$	−5.36714	−	9.29616i	−0.380466	−	0.658987i	−0.991129	+	0.132904i	$0.957570\pi$
$200$	−0.679295	−	0.319559i	−0.0480334	−	0.0225962i
$201$		0			0
$202$	−3.36925	−	16.4106i	−0.237060	−	1.15465i
$203$	13.4234	−	5.84531i	0.942140	−	0.410260i
$204$		0			0
$205$	6.98742	+	4.03419i	0.488023	+	0.281760i
$206$	1.52292	+	1.71517i	0.106107	+	0.119502i
$207$		0			0
$208$	12.7933	−	3.76737i	0.887059	−	0.261220i
$209$	−10.8254			−0.748807
$210$		0			0
$211$		−	0.556345i		−	0.0383004i	−0.999817	−	0.0191502i	$-0.993904\pi$
$211$		−	0.556345i		−	0.0383004i	0.999817	−	0.0191502i	$-0.00609607\pi$
$212$	14.0172	+	1.67039i	0.962706	+	0.114723i
$213$		0			0
$214$	5.31850	−	4.72234i	0.363565	−	0.322812i
$215$	−12.9034	+	22.3494i	−0.880007	+	1.52422i
$216$		0			0
$217$	−11.7050	+	15.8363i	−0.794587	+	1.07504i
$218$	−0.0581409	−	0.283187i	−0.00393780	−	0.0191798i
$219$		0			0
$220$	−14.2835	−	10.6838i	−0.962995	−	0.720300i
$221$	0.829044	−	0.478649i	0.0557676	−	0.0321974i
$222$		0			0
$223$	11.1076			0.743820			0.371910	−	0.928269i	$-0.378703\pi$
$223$	11.1076			0.743820			0.371910	+	0.928269i	$0.378703\pi$
$224$	−5.49543	−	13.9212i	−0.367179	−	0.930150i
$225$		0			0
$226$	6.65960	−	20.0220i	0.442990	−	1.33184i
$227$	−7.59321	+	4.38394i	−0.503979	+	0.290972i	−0.730355	−	0.683068i	$-0.760645\pi$
$227$	−7.59321	+	4.38394i	−0.503979	+	0.290972i	0.226376	+	0.974040i	$0.427312\pi$
$228$		0			0
$229$	−17.9235	−	10.3481i	−1.18442	−	0.683822i	−0.227383	−	0.973805i	$-0.573017\pi$
$229$	−17.9235	−	10.3481i	−1.18442	−	0.683822i	−0.957032	+	0.289983i	$0.906350\pi$
$230$	−4.26453	−	20.7712i	−0.281195	−	1.36961i
$231$		0			0
$232$	−8.93414	−	12.8514i	−0.586555	−	0.843739i
$233$	−2.86427	+	4.96105i	−0.187644	+	0.325009i	−0.944464	−	0.328614i	$-0.893419\pi$
$233$	−2.86427	+	4.96105i	−0.187644	+	0.325009i	0.756820	+	0.653623i	$0.226752\pi$
$234$		0			0
$235$	0.172903	−	0.0998258i	0.0112790	−	0.00651192i
$236$	8.64320	+	1.02998i	0.562624	+	0.0670461i
$237$		0			0
$238$	−0.618241	−	0.878587i	−0.0400746	−	0.0569504i
$239$	−2.27651			−0.147255			−0.0736276	−	0.997286i	$-0.523458\pi$
$239$	−2.27651			−0.147255			−0.0736276	+	0.997286i	$0.523458\pi$
$240$		0			0
$241$	−11.7925	−	20.4252i	−0.759623	−	1.31570i	−0.943043	−	0.332670i	$-0.892050\pi$
$241$	−11.7925	−	20.4252i	−0.759623	−	1.31570i	0.183421	−	0.983035i	$-0.441283\pi$
$242$	−3.85563	−	4.34237i	−0.247849	−	0.279138i
$243$		0			0
$244$	5.64786	+	13.1747i	0.361567	+	0.843425i
$245$	−15.3556	+	4.71285i	−0.981033	+	0.301093i
$246$		0			0
$247$	−4.64320	+	8.04226i	−0.295440	+	0.511717i
$248$	19.0496	+	8.96145i	1.20965	+	0.569052i
$249$		0			0
$250$	−14.5790	−	4.84918i	−0.922058	−	0.306689i
$251$		−	12.4322i		−	0.784716i	−0.919813	−	0.392358i	$-0.871659\pi$
$251$		−	12.4322i		−	0.784716i	0.919813	−	0.392358i	$-0.128341\pi$
$252$		0			0
$253$		−	25.3965i		−	1.59666i
$254$	−2.80870	+	8.44432i	−0.176234	+	0.529844i
$255$		0			0
$256$	−13.4465	+	8.67137i	−0.840404	+	0.541960i
$257$	0.141492	−	0.245072i	0.00882604	−	0.0152871i	−0.861579	−	0.507624i	$-0.830524\pi$
$257$	0.141492	−	0.245072i	0.00882604	−	0.0152871i	0.870405	+	0.492337i	$0.163857\pi$
$258$		0			0
$259$	1.77521	−	15.6562i	0.110306	−	0.972826i
$260$	−14.0635	+	6.02888i	−0.872183	+	0.373895i
$261$		0			0
$262$	1.31233	−	1.16523i	0.0810760	−	0.0719881i
$263$	7.15962	+	12.4008i	0.441481	+	0.764667i	0.997800	−	0.0663018i	$-0.0211200\pi$
$263$	7.15962	+	12.4008i	0.441481	+	0.764667i	−0.556319	+	0.830969i	$0.687787\pi$
$264$		0			0
$265$	−16.1961			−0.994918
$266$	9.45527	+	4.38234i	0.579740	+	0.268699i
$267$		0			0
$268$	−25.8680	−	3.08261i	−1.58014	−	0.188300i
$269$	14.5614	−	8.40704i	0.887825	−	0.512586i	0.0145946	−	0.999893i	$-0.495354\pi$
$269$	14.5614	−	8.40704i	0.887825	−	0.512586i	0.873230	+	0.487307i	$0.162021\pi$
$270$		0			0
$271$	−13.4228	+	23.2490i	−0.815378	+	1.41228i	0.0936779	+	0.995603i	$0.470138\pi$
$271$	−13.4228	+	23.2490i	−0.815378	+	1.41228i	−0.909056	+	0.416674i	$0.863196\pi$
$272$	−0.791892	+	0.831818i	−0.0480155	+	0.0504364i
$273$		0			0
$274$	2.20292	−	0.452281i	0.133083	−	0.0273233i
$275$	0.893374	+	0.515790i	0.0538725	+	0.0311033i
$276$		0			0
$277$	19.4881	−	11.2515i	1.17093	−	0.676036i	0.217030	−	0.976165i	$-0.430363\pi$
$277$	19.4881	−	11.2515i	1.17093	−	0.676036i	0.953899	+	0.300129i	$0.0970296\pi$
$278$	−1.38193	−	0.459649i	−0.0828825	−	0.0275679i
$279$		0			0
$280$	8.15072	+	15.1139i	0.487099	+	0.903226i
$281$	−12.8375			−0.765824			−0.382912	−	0.923785i	$-0.625079\pi$
$281$	−12.8375			−0.765824			−0.382912	+	0.923785i	$0.625079\pi$
$282$		0			0
$283$	−6.32017	+	3.64895i	−0.375695	+	0.216908i	−0.675944	−	0.736953i	$-0.736264\pi$
$283$	−6.32017	+	3.64895i	−0.375695	+	0.216908i	0.300249	+	0.953861i	$0.402930\pi$
$284$	−9.91096	−	7.41319i	−0.588107	−	0.439892i
$285$		0			0
$286$	−17.9519	+	3.68569i	−1.06152	+	0.217940i
$287$	−3.71414	−	8.52932i	−0.219239	−	0.503470i
$288$		0			0
$289$	8.45878	−	14.6510i	0.497575	−	0.861826i
$290$	11.9231	+	13.4283i	0.700147	+	0.788535i
$291$		0			0
$292$	3.28472	−	27.5641i	0.192224	−	1.61307i
$293$			9.95674i			0.581679i	0.956772	+	0.290840i	$0.0939346\pi$
$293$			9.95674i			0.581679i	−0.956772	+	0.290840i	$0.906065\pi$
$294$		0			0
$295$	−9.98671			−0.581449
$296$	−16.7851	+	1.41139i	−0.975617	+	0.0820354i
$297$		0			0
$298$	10.1434	−	9.00642i	0.587592	−	0.521728i
$299$	−18.8673	−	10.8930i	−1.09112	−	0.629959i
$300$		0			0
$301$	27.2812	−	11.8798i	1.57246	−	0.684738i
$302$	−9.68645	+	1.98872i	−0.557393	+	0.114438i
$303$		0			0
$304$	2.61810	−	10.8290i	0.150158	−	0.621087i
$305$	−8.22304	−	14.2427i	−0.470850	−	0.815536i
$306$		0			0
$307$			14.9479i			0.853122i	0.904459	+	0.426561i	$0.140275\pi$
$307$			14.9479i			0.853122i	−0.904459	+	0.426561i	$0.859725\pi$
$308$	5.92209	+	19.6953i	0.337442	+	1.12224i
$309$		0			0
$310$	−22.9192	−	7.62323i	−1.30172	−	0.432971i
$311$	−15.6295	−	27.0712i	−0.886270	−	1.53506i	−0.844251	−	0.535948i	$-0.819954\pi$
$311$	−15.6295	−	27.0712i	−0.886270	−	1.53506i	−0.0420192	−	0.999117i	$-0.513379\pi$
$312$		0			0
$313$	1.53234	−	2.65409i	0.0866130	−	0.150018i	−0.819464	−	0.573130i	$-0.805729\pi$
$313$	1.53234	−	2.65409i	0.0866130	−	0.150018i	0.906077	+	0.423112i	$0.139062\pi$
$314$	4.93692	+	24.0462i	0.278606	+	1.35701i
$315$		0			0
$316$	−16.5412	+	7.09104i	−0.930515	+	0.398902i
$317$	−14.1145	−	8.14904i	−0.792752	−	0.457695i	0.0481787	−	0.998839i	$-0.484658\pi$
$317$	−14.1145	−	8.14904i	−0.792752	−	0.457695i	−0.840930	+	0.541143i	$0.817992\pi$
$318$		0			0
$319$	10.7539	+	18.6263i	0.602104	+	1.04287i
$320$	14.1418	−	11.7045i	0.790552	−	0.654301i
$321$		0			0
$322$	−10.2810	+	22.1822i	−0.572940	+	1.23617i
$323$		−	0.799705i		−	0.0444968i
$324$		0			0
$325$	0.766369	−	0.442463i	0.0425105	−	0.0245434i
$326$	−16.6262	+	14.7625i	−0.920838	+	0.817620i
$327$		0			0
$328$	−8.16588	+	5.67680i	−0.450885	+	0.313449i
$329$	−0.228734	−	0.0259356i	−0.0126105	−	0.00142988i
$330$		0			0
$331$	2.39289	+	1.38153i	0.131525	+	0.0759359i	0.564319	−	0.825557i	$-0.309139\pi$
$331$	2.39289	+	1.38153i	0.131525	+	0.0759359i	−0.432794	+	0.901493i	$0.642472\pi$
$332$	21.1211	−	28.2375i	1.15917	−	1.54974i
$333$		0			0
$334$	0.0455557	−	0.136963i	0.00249270	−	0.00749427i
$335$	29.8890			1.63301
$336$		0			0
$337$	25.8259			1.40682			0.703412	−	0.710782i	$-0.251659\pi$
$337$	25.8259			1.40682			0.703412	+	0.710782i	$0.251659\pi$
$338$	0.840727	−	2.52764i	0.0457295	−	0.137485i
$339$		0			0
$340$	0.789244	−	1.05517i	0.0428028	−	0.0572246i
$341$	−25.0531	−	14.4644i	−1.35670	−	0.783291i
$342$		0			0
$343$	17.4680	+	6.15385i	0.943182	+	0.332276i
$344$	−18.1573	−	26.1187i	−0.978979	−	1.40823i
$345$		0			0
$346$	2.41934	−	2.14815i	0.130064	−	0.115485i
$347$	10.6309	−	6.13775i	0.570696	−	0.329492i	−0.186731	−	0.982411i	$-0.559789\pi$
$347$	10.6309	−	6.13775i	0.570696	−	0.329492i	0.757427	+	0.652919i	$0.226456\pi$
$348$		0			0
$349$			0.209753i			0.0112278i	0.999984	+	0.00561390i	$0.00178697\pi$
$349$			0.209753i			0.0112278i	−0.999984	+	0.00561390i	$0.998213\pi$
$350$	−0.571502	−	0.812166i	−0.0305481	−	0.0434121i
$351$		0			0
$352$	19.4108	−	10.3256i	1.03460	−	0.550356i
$353$	−9.79924	−	16.9728i	−0.521561	−	0.903370i	−0.999685	−	0.0250782i	$-0.992017\pi$
$353$	−9.79924	−	16.9728i	−0.521561	−	0.903370i	0.478124	−	0.878292i	$-0.341317\pi$
$354$		0			0
$355$	12.2976	+	7.10004i	0.652690	+	0.376831i
$356$	31.5876	−	13.5413i	1.67414	−	0.717686i
$357$		0			0
$358$	5.29676	+	25.7989i	0.279943	+	1.36351i
$359$	−2.85556	+	4.94598i	−0.150711	+	0.261039i	−0.931489	−	0.363770i	$-0.881490\pi$
$359$	−2.85556	+	4.94598i	−0.150711	+	0.261039i	0.780778	+	0.624808i	$0.214823\pi$
$360$		0			0
$361$	−5.62118	−	9.73617i	−0.295852	−	0.512430i
$362$	18.3557	+	6.10537i	0.964755	+	0.320891i
$363$		0			0
$364$	17.1719	+	4.04809i	0.900050	+	0.212177i
$365$			31.8487i			1.66704i
$366$		0			0
$367$	−14.0638	−	24.3591i	−0.734122	−	1.27154i	−0.955107	−	0.296260i	$-0.904261\pi$
$367$	−14.0638	−	24.3591i	−0.734122	−	1.27154i	0.220985	−	0.975277i	$-0.429073\pi$
$368$	25.4051	+	6.14210i	1.32433	+	0.320179i
$369$		0			0
$370$	18.9311	−	3.88674i	0.984181	−	0.202062i
$371$	15.0174	+	11.0997i	0.779666	+	0.576270i
$372$		0			0
$373$	14.8987	+	8.60176i	0.771425	+	0.445382i	0.833383	−	0.552697i	$-0.186401\pi$
$373$	14.8987	+	8.60176i	0.771425	+	0.445382i	−0.0619580	+	0.998079i	$0.519734\pi$
$374$	1.18012	−	1.04784i	0.0610228	−	0.0541826i
$375$		0			0
$376$	0.0206202	+	0.245229i	0.00106341	+	0.0126467i
$377$	18.4502			0.950234
$378$		0			0
$379$			10.1872i			0.523281i	0.965165	+	0.261640i	$0.0842635\pi$
$379$			10.1872i			0.523281i	−0.965165	+	0.261640i	$0.915737\pi$
$380$	−1.51253	+	12.6926i	−0.0775912	+	0.651115i
$381$		0			0
$382$	11.8635	+	13.3612i	0.606992	+	0.683619i
$383$	−9.92164	+	17.1848i	−0.506972	+	0.878102i	0.492995	+	0.870032i	$0.335902\pi$
$383$	−9.92164	+	17.1848i	−0.506972	+	0.878102i	−0.999967	+	0.00806963i	$0.997431\pi$
$384$		0			0
$385$	−9.42069	−	21.6341i	−0.480123	−	1.10258i
$386$	−3.60989	+	0.741145i	−0.183739	+	0.0377233i
$387$		0			0
$388$	−10.3545	−	7.74493i	−0.525669	−	0.393189i
$389$	16.0503	−	9.26666i	0.813784	−	0.469838i	−0.0344843	−	0.999405i	$-0.510979\pi$
$389$	16.0503	−	9.26666i	0.813784	−	0.469838i	0.848268	+	0.529567i	$0.177646\pi$
$390$		0			0
$391$	1.87612			0.0948794
$392$	2.80050	−	19.5999i	0.141446	−	0.989946i
$393$		0			0
$394$	1.06653	+	0.354744i	0.0537312	+	0.0178718i
$395$	17.8821	−	10.3242i	0.899746	−	0.519468i
$396$		0			0
$397$	6.91207	+	3.99068i	0.346907	+	0.200287i	0.663322	−	0.748334i	$-0.269146\pi$
$397$	6.91207	+	3.99068i	0.346907	+	0.200287i	−0.316415	+	0.948621i	$0.602479\pi$
$398$	−14.8704	+	3.05303i	−0.745385	+	0.153035i
$399$		0			0
$400$	−0.732025	+	0.768933i	−0.0366013	+	0.0384467i
$401$	18.0210	−	31.2132i	0.899925	−	1.55872i	0.0723360	−	0.997380i	$-0.476955\pi$
$401$	18.0210	−	31.2132i	0.899925	−	1.55872i	0.827589	−	0.561335i	$-0.189712\pi$
$402$		0			0
$403$	−21.4914	+	12.4081i	−1.07056	+	0.618091i
$404$	−23.5257	−	2.80348i	−1.17045	−	0.139479i
$405$		0			0
$406$	−1.85252	−	20.6223i	−0.0919390	−	1.02347i
$407$	23.1466			1.14734
$408$		0			0
$409$	14.7833	+	25.6054i	0.730987	+	1.26611i	0.956462	+	0.291858i	$0.0942735\pi$
$409$	14.7833	+	25.6054i	0.730987	+	1.26611i	−0.225474	+	0.974249i	$0.572393\pi$
$410$	8.53240	−	7.57599i	0.421385	−	0.374152i
$411$		0			0
$412$	2.98139	−	1.27809i	0.146882	−	0.0629669i
$413$	9.25993	+	6.84424i	0.455652	+	0.336783i
$414$		0			0
$415$	−20.2289	+	35.0374i	−0.992996	+	1.71992i
$416$	0.654693	−	18.8493i	0.0320990	−	0.924164i
$417$		0			0
$418$	−4.83185	+	14.5269i	−0.236333	+	0.710533i
$419$			8.73304i			0.426637i	0.976983	+	0.213318i	$0.0684271\pi$
$419$			8.73304i			0.426637i	−0.976983	+	0.213318i	$0.931573\pi$
$420$		0			0
$421$			1.77349i			0.0864344i	0.999066	+	0.0432172i	$0.0137607\pi$
$421$			1.77349i			0.0864344i	−0.999066	+	0.0432172i	$0.986239\pi$
$422$	−0.746576	−	0.248322i	−0.0363428	−	0.0120881i
$423$		0			0
$424$	8.49805	−	18.0646i	0.412702	−	0.877293i
$425$	−0.0381030	+	0.0659964i	−0.00184827	+	0.00320130i
$426$		0			0
$427$	−2.13642	+	18.8417i	−0.103389	+	0.911816i
$428$	−3.96316	−	9.24484i	−0.191567	−	0.446866i
$429$		0			0
$430$	24.2320	+	27.2910i	1.16857	+	1.31609i
$431$	14.1836	+	24.5667i	0.683200	+	1.18334i	0.973999	+	0.226553i	$0.0727456\pi$
$431$	14.1836	+	24.5667i	0.683200	+	1.18334i	−0.290799	+	0.956784i	$0.593921\pi$
$432$		0			0
$433$	−6.53217			−0.313916			−0.156958	−	0.987605i	$-0.550169\pi$
$433$	−6.53217			−0.313916			−0.156958	+	0.987605i	$0.550169\pi$
$434$	16.0268	+	22.7757i	0.769309	+	1.09327i
$435$		0			0
$436$	−0.405967	−	0.0483778i	−0.0194423	−	0.00231688i
$437$	−15.7613	+	9.09977i	−0.753964	+	0.435301i
$438$		0			0
$439$	−0.266161	+	0.461004i	−0.0127032	+	0.0220025i	−0.872307	−	0.488958i	$-0.837377\pi$
$439$	−0.266161	+	0.461004i	−0.0127032	+	0.0220025i	0.859604	+	0.510961i	$0.170710\pi$
$440$	−20.7123	+	14.3988i	−0.987418	+	0.686438i
$441$		0			0
$442$	−0.272274	−	1.32616i	−0.0129507	−	0.0630791i
$443$	7.37827	+	4.25985i	0.350552	+	0.202392i	0.664929	−	0.746907i	$-0.268462\pi$
$443$	7.37827	+	4.25985i	0.350552	+	0.202392i	−0.314376	+	0.949299i	$0.601795\pi$
$444$		0			0
$445$	−34.1482	+	19.7155i	−1.61878	+	0.934604i
$446$	4.95782	−	14.9056i	0.234760	−	0.705802i
$447$		0			0
$448$	−21.1342	+	1.16082i	−0.998495	+	0.0548438i
$449$	15.0180			0.708745			0.354373	−	0.935104i	$-0.384694\pi$
$449$	15.0180			0.708745			0.354373	+	0.935104i	$0.384694\pi$
$450$		0			0
$451$	11.8353	−	6.83310i	0.557302	−	0.321758i
$452$	−23.8956	−	17.8734i	−1.12396	−	0.840695i
$453$		0			0
$454$	2.49375	+	12.1463i	0.117038	+	0.570054i
$455$	−20.1129	−	2.28055i	−0.942905	−	0.106914i
$456$		0			0
$457$	15.7276	−	27.2410i	0.735705	−	1.27428i	−0.218708	−	0.975790i	$-0.570184\pi$
$457$	15.7276	−	27.2410i	0.735705	−	1.27428i	0.954413	−	0.298488i	$-0.0964823\pi$
$458$	−21.8865	+	19.4332i	−1.02269	+	0.908054i
$459$		0			0
$460$	−29.7769	−	3.54842i	−1.38836	−	0.165446i
$461$			4.36281i			0.203196i	0.994826	+	0.101598i	$0.0323956\pi$
$461$			4.36281i			0.203196i	−0.994826	+	0.101598i	$0.967604\pi$
$462$		0			0
$463$	13.9787			0.649646			0.324823	−	0.945775i	$-0.394695\pi$
$463$	13.9787			0.649646			0.324823	+	0.945775i	$0.394695\pi$
$464$	−21.2335	+	6.25281i	−0.985738	+	0.290279i
$465$		0			0
$466$	5.37894	+	6.05798i	0.249174	+	0.280631i
$467$	−14.3226	−	8.26916i	−0.662771	−	0.382651i	0.130561	−	0.991440i	$-0.458322\pi$
$467$	−14.3226	−	8.26916i	−0.662771	−	0.382651i	−0.793332	+	0.608789i	$0.791655\pi$
$468$		0			0
$469$	−27.7138	−	20.4840i	−1.27971	−	0.945862i
$470$	−0.0567847	−	0.276581i	−0.00261928	−	0.0127577i
$471$		0			0
$472$	5.24001	−	11.1388i	0.241191	−	0.512707i
$473$	21.8558	+	37.8554i	1.00493	+	1.74059i
$474$		0			0
$475$		−	0.739247i		−	0.0339190i
$476$	−1.45495	+	0.437483i	−0.0666876	+	0.0200520i
$477$		0			0
$478$	−1.01611	+	3.05492i	−0.0464757	+	0.139729i
$479$	−0.592007	−	1.02539i	−0.0270495	−	0.0468511i	0.852184	−	0.523243i	$-0.175278\pi$
$479$	−0.592007	−	1.02539i	−0.0270495	−	0.0468511i	−0.879233	+	0.476391i	$0.841945\pi$
$480$		0			0
$481$	9.92801	−	17.1958i	0.452679	−	0.784062i
$482$	−32.6728	+	6.70803i	−1.48820	+	0.305542i
$483$		0			0
$484$	−7.54810	+	3.23579i	−0.343096	+	0.147081i
$485$	12.8480	+	7.41778i	0.583396	+	0.336824i
$486$		0			0
$487$	12.0448	+	20.8622i	0.545801	+	0.945356i	0.998556	+	0.0537205i	$0.0171080\pi$
$487$	12.0448	+	20.8622i	0.545801	+	0.945356i	−0.452755	+	0.891635i	$0.649559\pi$
$488$	20.2005	−	1.69857i	0.914432	−	0.0768906i
$489$		0			0
$490$	−0.529574	+	22.7097i	−0.0239237	+	1.02592i
$491$			18.4971i			0.834761i	0.908732	+	0.417381i	$0.137052\pi$
$491$			18.4971i			0.834761i	−0.908732	+	0.417381i	$0.862948\pi$
$492$		0			0
$493$	−1.37599	+	0.794427i	−0.0619714	+	0.0357792i
$494$	8.71968	+	9.82047i	0.392317	+	0.441844i
$495$		0			0
$496$	20.5283	−	21.5633i	0.921749	−	0.968223i
$497$	−6.53677	−	15.0113i	−0.293214	−	0.673350i
$498$		0			0
$499$	−10.5034	−	6.06414i	−0.470197	−	0.271468i	0.246125	−	0.969238i	$-0.420843\pi$
$499$	−10.5034	−	6.06414i	−0.470197	−	0.271468i	−0.716322	+	0.697770i	$0.754176\pi$
$500$	−13.0145	+	17.3996i	−0.582028	+	0.778134i
$501$		0			0
$502$	−16.6832	−	5.54907i	−0.744608	−	0.247667i
$503$	7.61078			0.339348			0.169674	−	0.985500i	$-0.445729\pi$
$503$	7.61078			0.339348			0.169674	+	0.985500i	$0.445729\pi$
$504$		0			0
$505$	27.1826			1.20961
$506$	−34.0803	−	11.3356i	−1.51505	−	0.503928i
$507$		0			0
$508$	10.0780	+	7.53816i	0.447141	+	0.334452i
$509$	13.9392	+	8.04779i	0.617844	+	0.356712i	0.776029	−	0.630697i	$-0.217231\pi$
$509$	13.9392	+	8.04779i	0.617844	+	0.356712i	−0.158185	+	0.987409i	$0.550564\pi$
$510$		0			0
$511$	21.8270	−	29.5309i	0.965571	−	1.30637i
$512$	5.63461	+	21.9146i	0.249017	+	0.968499i
$513$		0			0
$514$	−0.265715	−	0.299259i	−0.0117202	−	0.0131997i
$515$	−3.22307	+	1.86084i	−0.142025	+	0.0819985i
$516$		0			0
$517$		−	0.338169i		−	0.0148727i
$518$	−20.2171	−	9.37025i	−0.888288	−	0.411705i
$519$		0			0
$520$	1.81316	+	21.5632i	0.0795123	+	0.945610i
$521$	−9.64668	−	16.7085i	−0.422629	−	0.732015i	0.573567	−	0.819159i	$-0.305559\pi$
$521$	−9.64668	−	16.7085i	−0.422629	−	0.732015i	−0.996196	+	0.0871440i	$0.972226\pi$
$522$		0			0
$523$	−27.9337	−	16.1275i	−1.22146	−	0.705208i	−0.256227	−	0.966617i	$-0.582480\pi$
$523$	−27.9337	−	16.1275i	−1.22146	−	0.705208i	−0.965228	+	0.261409i	$0.915813\pi$
$524$	−0.977904	−	2.28115i	−0.0427199	−	0.0996524i
$525$		0			0
$526$	19.8367	−	4.07266i	0.864921	−	0.177577i
$527$	1.06853	−	1.85075i	0.0465459	−	0.0806199i
$528$		0			0
$529$	−9.84821	−	17.0576i	−0.428183	−	0.741635i
$530$	−7.22904	+	21.7340i	−0.314009	+	0.944065i
$531$		0			0
$532$	10.1011	−	10.7323i	0.437938	−	0.465303i
$533$		−	11.7234i		−	0.507796i
$534$		0			0
$535$	5.77019	+	9.99426i	0.249467	+	0.432090i
$536$	−15.6827	+	33.3372i	−0.677390	+	1.43995i
$537$		0			0
$538$	−4.78224	−	23.2928i	−0.206177	−	1.00423i
$539$	−6.09149	+	26.5160i	−0.262379	+	1.14213i
$540$		0			0
$541$	3.45438	+	1.99439i	0.148515	+	0.0857454i	0.572416	−	0.819963i	$-0.306006\pi$
$541$	3.45438	+	1.99439i	0.148515	+	0.0857454i	−0.423901	+	0.905709i	$0.639340\pi$
$542$	25.2073	+	28.3896i	1.08275	+	1.21944i
$543$		0			0
$544$	0.762785	+	1.43394i	0.0327041	+	0.0614797i
$545$	0.469072			0.0200928
$546$		0			0
$547$		−	12.1824i		−	0.520882i	−0.965490	−	0.260441i	$-0.916132\pi$
$547$		−	12.1824i		−	0.520882i	0.965490	−	0.260441i	$-0.0838679\pi$
$548$	0.376333	−	3.15804i	0.0160761	−	0.134905i
$549$		0			0
$550$	1.09091	−	0.968626i	0.0465164	−	0.0413023i
$551$	7.70644	−	13.3479i	0.328305	−	0.568642i
$552$		0			0
$553$	−23.6563	−	2.68233i	−1.00597	−	0.114064i
$554$	−6.40027	−	31.1738i	−0.271922	−	1.32445i
$555$		0			0
$556$	−1.23363	+	1.64929i	−0.0523177	+	0.0699454i
$557$	2.58791	−	1.49413i	0.109653	−	0.0633084i	−0.444170	−	0.895942i	$-0.646502\pi$
$557$	2.58791	−	1.49413i	0.109653	−	0.0633084i	0.553824	+	0.832634i	$0.313168\pi$
$558$		0			0
$559$	37.4974			1.58597
$560$	23.9198	−	4.19171i	1.01080	−	0.177132i
$561$		0			0
$562$	−5.72997	+	17.2271i	−0.241704	+	0.726681i
$563$	−3.82170	+	2.20646i	−0.161065	+	0.0929911i	−0.578366	−	0.815777i	$-0.696309\pi$
$563$	−3.82170	+	2.20646i	−0.161065	+	0.0929911i	0.417301	+	0.908768i	$0.362976\pi$
$564$		0			0
$565$	29.6500	+	17.1184i	1.24738	+	0.720177i
$566$	2.07566	+	10.1099i	0.0872466	+	0.424952i
$567$		0			0
$568$	−14.3717	+	9.99098i	−0.603022	+	0.419212i
$569$	−6.15432	+	10.6596i	−0.258002	+	0.446873i	−0.965707	−	0.259635i	$-0.916398\pi$
$569$	−6.15432	+	10.6596i	−0.258002	+	0.446873i	0.707704	+	0.706509i	$0.249731\pi$
$570$		0			0
$571$	−26.2766	+	15.1708i	−1.09964	+	0.634877i	−0.936126	−	0.351664i	$-0.885616\pi$
$571$	−26.2766	+	15.1708i	−1.09964	+	0.634877i	−0.163513	+	0.986541i	$0.552283\pi$
$572$	−3.06678	+	25.7353i	−0.128229	+	1.07604i
$573$		0			0
$574$	−13.1035	+	1.17710i	−0.546931	+	0.0491313i
$575$	1.73429			0.0723247
$576$		0			0
$577$	6.02559	+	10.4366i	0.250848	+	0.434482i	0.963760	−	0.266772i	$-0.0859571\pi$
$577$	6.02559	+	10.4366i	0.250848	+	0.434482i	−0.712911	+	0.701254i	$0.752624\pi$
$578$	−15.8851	−	17.8905i	−0.660735	−	0.744147i
$579$		0			0
$580$	23.3416	−	10.0063i	0.969208	−	0.415489i
$581$	42.7691	−	18.6241i	1.77436	−	0.772656i
$582$		0			0
$583$	−13.7164	+	23.7576i	−0.568077	+	0.983939i
$584$	−35.5230	−	16.7110i	−1.46995	−	0.691505i
$585$		0			0
$586$	13.3613	+	4.44414i	0.551948	+	0.183586i
$587$		−	5.34331i		−	0.220542i	−0.993902	−	0.110271i	$-0.964828\pi$
$587$		−	5.34331i		−	0.220542i	0.993902	−	0.110271i	$-0.0351719\pi$
$588$		0			0
$589$			20.7309i			0.854200i
$590$	−4.45752	+	13.4015i	−0.183513	+	0.551730i
$591$		0			0
$592$	−5.59797	+	23.1545i	−0.230075	+	0.951642i
$593$	4.74530	−	8.21910i	0.194866	−	0.337518i	−0.751991	−	0.659174i	$-0.770906\pi$
$593$	4.74530	−	8.21910i	0.194866	−	0.337518i	0.946857	+	0.321656i	$0.104239\pi$
$594$		0			0
$595$	1.59818	−	0.695937i	0.0655190	−	0.0285306i
$596$	−7.55853	−	17.6317i	−0.309609	−	0.722223i
$597$		0			0
$598$	−23.0390	+	20.4565i	−0.942134	+	0.836529i
$599$	−3.86976	−	6.70262i	−0.158114	−	0.273861i	0.776075	−	0.630641i	$-0.217208\pi$
$599$	−3.86976	−	6.70262i	−0.158114	−	0.273861i	−0.934189	+	0.356780i	$0.883875\pi$
$600$		0			0
$601$	−19.0198			−0.775835			−0.387917	−	0.921694i	$-0.626805\pi$
$601$	−19.0198			−0.775835			−0.387917	+	0.921694i	$0.626805\pi$
$602$	−3.76498	−	41.9119i	−0.153449	−	1.70820i
$603$		0			0
$604$	−1.65477	+	13.8862i	−0.0673317	+	0.565021i
$605$	8.15998	−	4.71117i	0.331751	−	0.191536i
$606$		0			0
$607$	−4.59791	+	7.96381i	−0.186623	+	0.323241i	−0.944122	−	0.329595i	$-0.893088\pi$
$607$	−4.59791	+	7.96381i	−0.186623	+	0.323241i	0.757499	+	0.652836i	$0.226421\pi$
$608$	−13.3632	−	8.34678i	−0.541950	−	0.338507i
$609$		0			0
$610$	−22.7830	+	4.67758i	−0.922459	+	0.189390i
$611$	−0.251229	−	0.145047i	−0.0101636	−	0.00586798i
$612$		0			0
$613$	−22.8688	+	13.2033i	−0.923663	+	0.533277i	−0.884802	−	0.465967i	$-0.845706\pi$
$613$	−22.8688	+	13.2033i	−0.923663	+	0.533277i	−0.0388615	+	0.999245i	$0.512373\pi$
$614$	20.0590	+	6.67192i	0.809517	+	0.269257i
$615$		0			0
$616$	29.0729	+	0.843848i	1.17138	+	0.0339996i
$617$	45.5837			1.83513			0.917565	−	0.397585i	$-0.130152\pi$
$617$	45.5837			1.83513			0.917565	+	0.397585i	$0.130152\pi$
$618$		0			0
$619$	42.4644	−	24.5168i	1.70679	−	0.985415i	0.768310	−	0.640078i	$-0.221098\pi$
$619$	42.4644	−	24.5168i	1.70679	−	0.985415i	0.938479	−	0.345337i	$-0.112235\pi$
$620$	−20.4597	+	27.3533i	−0.821681	+	1.09854i
$621$		0			0
$622$	−43.3038	+	8.89068i	−1.73632	+	0.356484i
$623$	45.1748	+	5.12226i	1.80989	+	0.205219i
$624$		0			0
$625$	13.1283	−	22.7389i	0.525133	−	0.909556i
$626$	−2.87765	−	3.24094i	−0.115014	−	0.129534i
$627$		0			0
$628$	34.4719	+	4.10790i	1.37558	+	0.163923i
$629$			1.70992i			0.0681788i
$630$		0			0
$631$	−12.5801			−0.500804			−0.250402	−	0.968142i	$-0.580563\pi$
$631$	−12.5801			−0.500804			−0.250402	+	0.968142i	$0.580563\pi$
$632$	2.13260	+	25.3622i	0.0848301	+	1.00885i
$633$		0			0
$634$	−17.2354	+	15.3034i	−0.684505	+	0.607778i
$635$	−12.5049	−	7.21973i	−0.496244	−	0.286506i
$636$		0			0
$637$	17.0862	+	15.8986i	0.676980	+	0.629926i
$638$	29.7952	−	6.11724i	1.17960	−	0.242184i
$639$		0			0
$640$	−9.39449	−	24.2016i	−0.371350	−	0.956652i
$641$	−17.1129	−	29.6404i	−0.675920	−	1.17073i	−0.976199	−	0.216876i	$-0.930413\pi$
$641$	−17.1129	−	29.6404i	−0.675920	−	1.17073i	0.300280	−	0.953851i	$-0.402920\pi$
$642$		0			0
$643$		−	23.0442i		−	0.908776i	−0.890804	−	0.454388i	$-0.849858\pi$
$643$		−	23.0442i		−	0.908776i	0.890804	−	0.454388i	$-0.150142\pi$
$644$	25.1781	+	23.6974i	0.992155	+	0.933806i
$645$		0			0
$646$	−1.07315	−	0.356944i	−0.0422224	−	0.0140438i
$647$	7.79098	+	13.4944i	0.306295	+	0.530519i	0.977549	−	0.210709i	$-0.0675773\pi$
$647$	7.79098	+	13.4944i	0.306295	+	0.530519i	−0.671254	+	0.741228i	$0.734244\pi$
$648$		0			0
$649$	−8.45774	+	14.6492i	−0.331995	+	0.575033i
$650$	−0.251690	−	1.22590i	−0.00987210	−	0.0480839i
$651$		0			0
$652$	12.3893	+	28.9003i	0.485201	+	1.13182i
$653$	−42.6318	−	24.6135i	−1.66831	−	0.963199i	−0.968549	−	0.248822i	$-0.919957\pi$
$653$	−42.6318	−	24.6135i	−1.66831	−	0.963199i	−0.699761	−	0.714377i	$-0.746710\pi$
$654$		0			0
$655$	1.42378	+	2.46607i	0.0556319	+	0.0963572i
$656$	3.97307	+	13.4919i	0.155122	+	0.526768i
$657$		0			0
$658$	−0.136898	+	0.295369i	−0.00533685	+	0.0115147i
$659$			5.33204i			0.207707i	0.994593	+	0.103853i	$0.0331173\pi$
$659$			5.33204i			0.207707i	−0.994593	+	0.103853i	$0.966883\pi$
$660$		0			0
$661$	33.5057	−	19.3445i	1.30322	−	0.752416i	0.322267	−	0.946649i	$-0.395555\pi$
$661$	33.5057	−	19.3445i	1.30322	−	0.752416i	0.980955	+	0.194233i	$0.0622219\pi$
$662$	2.92197	−	2.59445i	0.113566	−	0.100836i
$663$		0			0
$664$	−28.4655	−	40.9467i	−1.10468	−	1.58904i
$665$	−10.0508	+	13.5982i	−0.389753	+	0.527317i
$666$		0			0
$667$	31.3145	+	18.0794i	1.21250	+	0.700038i
$668$	−0.163461	−	0.122265i	−0.00632449	−	0.00473058i
$669$		0			0
$670$	13.3408	−	40.1090i	0.515400	−	1.54954i
$671$	−27.8563			−1.07538
$672$		0			0
$673$	−9.56678			−0.368772			−0.184386	−	0.982854i	$-0.559030\pi$
$673$	−9.56678			−0.368772			−0.184386	+	0.982854i	$0.559030\pi$
$674$	11.5272	−	34.6565i	0.444013	−	1.33492i
$675$		0			0
$676$	−3.01666	−	2.25639i	−0.116025	−	0.0867844i
$677$	15.3536	+	8.86439i	0.590086	+	0.340686i	0.765131	−	0.643874i	$-0.222674\pi$
$677$	15.3536	+	8.86439i	0.590086	+	0.340686i	−0.175046	+	0.984560i	$0.556007\pi$
$678$		0			0
$679$	−6.82930	−	15.6831i	−0.262084	−	0.601862i
$680$	−1.06369	−	1.53008i	−0.0407906	−	0.0586759i
$681$		0			0
$682$	−30.5925	+	27.1634i	−1.17145	+	1.04014i
$683$	−7.59766	+	4.38651i	−0.290716	+	0.167845i	−0.638265	−	0.769817i	$-0.720348\pi$
$683$	−7.59766	+	4.38651i	−0.290716	+	0.167845i	0.347549	+	0.937662i	$0.387014\pi$
$684$		0			0
$685$			3.64893i			0.139418i
$686$	16.0548	−	20.6941i	0.612974	−	0.790103i
$687$		0			0
$688$	−43.1539	+	12.7079i	−1.64523	+	0.484485i
$689$	11.7665	+	20.3801i	0.448267	+	0.776421i
$690$		0			0
$691$	18.5176	+	10.6911i	0.704443	+	0.406710i	0.809000	−	0.587809i	$-0.200009\pi$
$691$	18.5176	+	10.6911i	0.704443	+	0.406710i	−0.104557	+	0.994519i	$0.533343\pi$
$692$	−1.80281	−	4.20540i	−0.0685326	−	0.159865i
$693$		0			0
$694$	−3.49139	−	17.0055i	−0.132531	−	0.645519i
$695$	1.18152	−	2.04646i	0.0448177	−	0.0776265i
$696$		0			0
$697$	0.504783	+	0.874310i	0.0191200	+	0.0331169i
$698$	0.281473	+	0.0936220i	0.0106539	+	0.00354364i
$699$		0			0
$700$	−1.34496	+	0.404410i	−0.0508346	+	0.0152853i
$701$			13.4233i			0.506990i	0.967337	+	0.253495i	$0.0815802\pi$
$701$			13.4233i			0.506990i	−0.967337	+	0.253495i	$0.918420\pi$
$702$		0			0
$703$	−8.29363	−	14.3650i	−0.312800	−	0.541786i
$704$	−5.19230	−	30.6568i	−0.195692	−	1.15542i
$705$		0			0
$706$	−27.1501	+	5.57418i	−1.02181	+	0.209787i
$707$	−25.2044	−	18.6292i	−0.947910	−	0.700623i
$708$		0			0
$709$	−43.8660	−	25.3260i	−1.64742	−	0.951139i	−0.978092	−	0.208174i	$-0.933248\pi$
$709$	−43.8660	−	25.3260i	−1.64742	−	0.951139i	−0.669330	−	0.742965i	$-0.733419\pi$
$710$	15.0167	−	13.3335i	0.563568	−	0.500397i
$711$		0			0
$712$	−4.07247	−	48.4324i	−0.152622	−	1.81508i
$713$	−48.6349			−1.82139
$714$		0			0
$715$		−	29.7356i		−	1.11205i
$716$	36.9845	+	4.40732i	1.38218	+	0.164709i
$717$		0			0
$718$	5.36259	+	6.03957i	0.200130	+	0.225395i
$719$	14.4800	−	25.0801i	0.540013	−	0.935330i	−0.458890	−	0.888493i	$-0.651753\pi$
$719$	14.4800	−	25.0801i	0.540013	−	0.935330i	0.998903	−	0.0468366i	$-0.0149140\pi$
$720$		0			0
$721$	4.26381	+	0.483463i	0.158793	+	0.0180051i
$722$	−15.5742	+	3.19754i	−0.579613	+	0.119000i
$723$		0			0
$724$	16.3860	−	21.9070i	0.608979	−	0.814167i
$725$	−1.27196	+	0.734368i	−0.0472395	+	0.0272738i
$726$		0			0
$727$	−10.5092			−0.389766			−0.194883	−	0.980827i	$-0.562433\pi$
$727$	−10.5092			−0.389766			−0.194883	+	0.980827i	$0.562433\pi$
$728$	13.0968	−	21.2366i	0.485400	−	0.787080i
$729$		0			0
$730$	42.7388	+	14.2155i	1.58183	+	0.526140i
$731$	−2.79650	+	1.61456i	−0.103432	+	0.0597166i
$732$		0			0
$733$	24.3360	+	14.0504i	0.898871	+	0.518963i	0.876834	−	0.480794i	$-0.159651\pi$
$733$	24.3360	+	14.0504i	0.898871	+	0.518963i	0.0220370	+	0.999757i	$0.492985\pi$
$734$	−38.9655	+	8.00000i	−1.43824	+	0.295285i
$735$		0			0
$736$	19.5817	−	31.3503i	0.721791	−	1.15559i
$737$	25.3130	−	43.8434i	0.932415	−	1.61499i
$738$		0			0
$739$	30.1856	−	17.4276i	1.11039	−	0.641086i	0.171463	−	0.985191i	$-0.445151\pi$
$739$	30.1856	−	17.4276i	1.11039	−	0.641086i	0.938931	+	0.344104i	$0.111817\pi$
$740$	3.23407	−	27.1390i	0.118887	−	0.997651i
$741$		0			0
$742$	21.5980	−	15.1980i	0.792888	−	0.557937i
$743$	−38.4805			−1.41171			−0.705857	−	0.708354i	$-0.749438\pi$
$743$	−38.4805			−1.41171			−0.705857	+	0.708354i	$0.749438\pi$
$744$		0			0
$745$	11.0049	+	19.0610i	0.403188	+	0.698342i
$746$	18.1929	−	16.1536i	0.666090	−	0.591427i
$747$		0			0
$748$	−0.879389	−	2.05134i	−0.0321536	−	0.0750045i
$749$	1.49915	−	13.2214i	0.0547777	−	0.483101i
$750$		0			0
$751$	−0.0112661	+	0.0195135i	−0.000411106	+	0.000712057i	−0.866231	−	0.499644i	$-0.833464\pi$
$751$	−0.0112661	+	0.0195135i	−0.000411106	+	0.000712057i	0.865820	+	0.500356i	$0.166798\pi$
$752$	0.338284	+	0.0817857i	0.0123359	+	0.00298242i
$753$		0			0
$754$	8.23516	−	24.7589i	0.299907	−	0.901666i
$755$		−	16.0447i		−	0.583926i
$756$		0			0
$757$			30.0479i			1.09211i	0.837749	+	0.546055i	$0.183871\pi$
$757$			30.0479i			1.09211i	−0.837749	+	0.546055i	$0.816129\pi$
$758$	13.6705	+	4.54700i	0.496535	+	0.165155i
$759$		0			0
$760$	16.3574	+	7.69497i	0.593346	+	0.279126i
$761$	−8.58063	+	14.8621i	−0.311048	+	0.538751i	−0.978589	−	0.205822i	$-0.934013\pi$
$761$	−8.58063	+	14.8621i	−0.311048	+	0.538751i	0.667542	+	0.744572i	$0.267347\pi$
$762$		0			0
$763$	−0.434935	−	0.321471i	−0.0157457	−	0.0116380i
$764$	23.2250	−	9.95633i	0.840253	−	0.360207i
$765$		0			0
$766$	18.6323	+	20.9845i	0.673213	+	0.758200i
$767$	7.25536	+	12.5666i	0.261976	+	0.453755i
$768$		0			0
$769$	−47.2945			−1.70548			−0.852742	−	0.522332i	$-0.825062\pi$
$769$	−47.2945			−1.70548			−0.852742	+	0.522332i	$0.825062\pi$
$770$	−33.2363	+	2.98565i	−1.19775	+	0.107595i
$771$		0			0
$772$	−0.616691	+	5.17503i	−0.0221952	+	0.186253i
$773$	−37.0445	+	21.3877i	−1.33240	+	0.769260i	−0.985667	−	0.168704i	$-0.946042\pi$
$773$	−37.0445	+	21.3877i	−1.33240	+	0.769260i	−0.346731	+	0.937964i	$0.612708\pi$
$774$		0			0
$775$	0.987751	−	1.71083i	0.0354810	−	0.0614550i
$776$	−15.0148	+	10.4381i	−0.539001	+	0.374705i
$777$		0			0
$778$	−5.27123	−	25.6745i	−0.188983	−	0.920477i
$779$	−8.48136	−	4.89672i	−0.303876	−	0.175443i
$780$		0			0
$781$	20.8297	−	12.0260i	0.745345	−	0.430325i
$782$	0.837396	−	2.51762i	0.0299452	−	0.0900300i
$783$		0			0
$784$	−25.0517	−	12.5064i	−0.894705	−	0.446657i
$785$	−39.8303			−1.42160
$786$		0			0
$787$	−42.8358	+	24.7312i	−1.52693	+	0.881574i	−0.527442	+	0.849591i	$0.676849\pi$
$787$	−42.8358	+	24.7312i	−1.52693	+	0.881574i	−0.999488	+	0.0319826i	$0.989818\pi$
$788$	0.952084	−	1.27288i	0.0339166	−	0.0453444i
$789$		0			0
$790$	−5.87282	−	28.6047i	−0.208945	−	1.01771i
$791$	−15.7604	−	36.1928i	−0.560374	−	1.28687i
$792$		0			0
$793$	−11.9481	+	20.6947i	−0.424289	+	0.734890i
$794$	8.44038	−	7.49429i	0.299538	−	0.265962i
$795$		0			0
$796$	−2.54036	+	21.3177i	−0.0900408	+	0.755587i
$797$		−	13.3755i		−	0.473783i	−0.971536	−	0.236892i	$-0.923871\pi$
$797$		−	13.3755i		−	0.473783i	0.971536	−	0.236892i	$-0.0761286\pi$
$798$		0			0
$799$	0.0249817			0.000883788
$800$	0.705119	+	1.32554i	0.0249297	+	0.0468648i
$801$		0			0
$802$	−33.8424	−	38.1148i	−1.19502	−	1.34588i
$803$	46.7180	+	26.9727i	1.64864	+	0.951845i
$804$		0			0
$805$	−31.9017	−	23.5793i	−1.12439	−	0.831061i
$806$	7.05819	+	34.3783i	0.248614	+	1.21092i
$807$		0			0
$808$	−14.2627	+	30.3186i	−0.501759	+	1.06660i
$809$	7.11266	+	12.3195i	0.250068	+	0.433130i	0.963544	−	0.267549i	$-0.0862138\pi$
$809$	7.11266	+	12.3195i	0.250068	+	0.433130i	−0.713476	+	0.700679i	$0.752880\pi$
$810$		0			0
$811$		−	20.7849i		−	0.729855i	−0.931036	−	0.364928i	$-0.881094\pi$
$811$		−	20.7849i		−	0.729855i	0.931036	−	0.364928i	$-0.118906\pi$
$812$	−28.5006	−	6.71872i	−1.00017	−	0.235781i
$813$		0			0
$814$	10.3314	−	31.0612i	0.362115	−	1.08869i
$815$	−18.0382	−	31.2431i	−0.631851	−	1.09440i
$816$		0			0
$817$	15.6622	−	27.1278i	0.547952	−	0.949081i
$818$	40.9591	−	8.40931i	1.43210	−	0.294025i
$819$		0			0
$820$	−6.35806	−	14.8314i	−0.222033	−	0.517935i
$821$	−4.29903	−	2.48205i	−0.150037	−	0.0866241i	0.423102	−	0.906082i	$-0.360941\pi$
$821$	−4.29903	−	2.48205i	−0.150037	−	0.0866241i	−0.573139	+	0.819458i	$0.694275\pi$
$822$		0			0
$823$	−4.91749	−	8.51734i	−0.171413	−	0.296896i	0.767501	−	0.641048i	$-0.221500\pi$
$823$	−4.91749	−	8.51734i	−0.171413	−	0.296896i	−0.938914	+	0.344152i	$0.888167\pi$
$824$	−0.384379	−	4.57128i	−0.0133905	−	0.159248i
$825$		0			0
$826$	13.3176	−	9.37129i	0.463379	−	0.326069i
$827$			41.4331i			1.44077i	0.693574	+	0.720385i	$0.256035\pi$
$827$			41.4331i			1.44077i	−0.693574	+	0.720385i	$0.743965\pi$
$828$		0			0
$829$	−21.6531	+	12.5014i	−0.752044	+	0.434193i	−0.826432	−	0.563036i	$-0.809633\pi$
$829$	−21.6531	+	12.5014i	−0.752044	+	0.434193i	0.0743878	+	0.997229i	$0.476300\pi$
$830$	37.9887	+	42.7845i	1.31861	+	1.48507i
$831$		0			0
$832$	−25.0022	−	9.29185i	−0.866797	−	0.322137i
$833$	−1.95882	−	0.449998i	−0.0678692	−	0.0155915i
$834$		0			0
$835$	0.202824	+	0.117100i	0.00701901	+	0.00405243i
$836$	17.3374	+	12.9680i	0.599627	+	0.448508i
$837$		0			0
$838$	11.7191	+	3.89794i	0.404830	+	0.134652i
$839$	−2.43551			−0.0840833			−0.0420416	−	0.999116i	$-0.513386\pi$
$839$	−2.43551			−0.0840833			−0.0420416	+	0.999116i	$0.513386\pi$
$840$		0			0
$841$	−1.62232			−0.0559420
$842$	2.37989	+	0.791586i	0.0820166	+	0.0272799i
$843$		0			0
$844$	−0.666461	+	0.891016i	−0.0229405	+	0.0306700i
$845$	3.74310	+	2.16108i	0.128767	+	0.0743434i
$846$		0			0
$847$	−10.7949	−	1.22400i	−0.370916	−	0.0420573i
$848$	−20.4483	−	19.4668i	−0.702198	−	0.668493i
$849$		0			0
$850$	0.0715555	+	0.0805888i	0.00245433	+	0.00276417i
$851$	33.7005	−	19.4570i	1.15524	−	0.666977i
$852$		0			0
$853$		−	51.1404i		−	1.75101i	−0.483206	−	0.875507i	$-0.660528\pi$
$853$		−	51.1404i		−	1.75101i	0.483206	−	0.875507i	$-0.339472\pi$
$854$	24.3307	+	11.2768i	0.832580	+	0.385886i
$855$		0			0
$856$	−14.1749	+	1.19190i	−0.484487	+	0.0407384i
$857$	26.7314	+	46.3001i	0.913127	+	1.58158i	0.809621	+	0.586954i	$0.199673\pi$
$857$	26.7314	+	46.3001i	0.913127	+	1.58158i	0.103506	+	0.994629i	$0.466994\pi$
$858$		0			0
$859$	14.3724	+	8.29790i	0.490380	+	0.283121i	0.724732	−	0.689031i	$-0.241964\pi$
$859$	14.3724	+	8.29790i	0.490380	+	0.283121i	−0.234352	+	0.972152i	$0.575297\pi$
$860$	47.4385	−	20.3364i	1.61764	−	0.693464i
$861$		0			0
$862$	39.2976	−	8.06817i	1.33848	−	0.274803i
$863$	−20.4256	+	35.3782i	−0.695296	+	1.20429i	0.274785	+	0.961506i	$0.411393\pi$
$863$	−20.4256	+	35.3782i	−0.695296	+	1.20429i	−0.970081	+	0.242782i	$0.921940\pi$
$864$		0			0
$865$	2.62481	+	4.54631i	0.0892463	+	0.154579i
$866$	−2.91560	+	8.76572i	−0.0990762	+	0.297871i
$867$		0			0
$868$	37.7169	−	11.3409i	1.28020	−	0.384937i
$869$		−	34.9743i		−	1.18642i
$870$		0			0
$871$	−21.7144	−	37.6104i	−0.735764	−	1.27438i
$872$	−0.246121	+	0.523187i	−0.00833471	+	0.0177173i
$873$		0			0
$874$	5.17630	+	25.2122i	0.175091	+	0.852814i
$875$	−26.3538	+	11.4759i	−0.890920	+	0.387956i
$876$		0			0
$877$	1.31595	+	0.759763i	0.0444364	+	0.0256554i	0.522054	−	0.852913i	$-0.325166\pi$
$877$	1.31595	+	0.759763i	0.0444364	+	0.0256554i	−0.477617	+	0.878568i	$0.658499\pi$
$878$	0.499836	+	0.562936i	0.0168686	+	0.0189982i
$879$		0			0
$880$	10.0774	+	34.2212i	0.339710	+	1.15360i
$881$	−12.3299			−0.415406			−0.207703	−	0.978192i	$-0.566599\pi$
$881$	−12.3299			−0.415406			−0.207703	+	0.978192i	$0.566599\pi$
$882$		0			0
$883$			12.0145i			0.404319i	0.979353	+	0.202159i	$0.0647959\pi$
$883$			12.0145i			0.404319i	−0.979353	+	0.202159i	$0.935204\pi$
$884$	−1.90115	−	0.226553i	−0.0639424	−	0.00761981i
$885$		0			0
$886$	9.00967	−	7.99977i	0.302686	−	0.268757i
$887$	−11.5240	+	19.9601i	−0.386938	+	0.670196i	−0.992036	−	0.125955i	$-0.959800\pi$
$887$	−11.5240	+	19.9601i	−0.386938	+	0.670196i	0.605098	+	0.796151i	$0.293134\pi$
$888$		0			0
$889$	6.64697	+	15.2644i	0.222932	+	0.511951i
$890$	11.2149	+	54.6244i	0.375925	+	1.83102i
$891$		0			0
$892$	−17.7894	−	13.3061i	−0.595634	−	0.445521i
$893$	−0.209871	+	0.121169i	−0.00702306	+	0.00405476i
$894$		0			0
$895$	−42.7335			−1.42842
$896$	−7.87538	+	28.8787i	−0.263098	+	0.964769i
$897$		0			0
$898$	6.70323	−	20.1532i	0.223690	−	0.672520i
$899$	35.6699	−	20.5940i	1.18966	−	0.686850i
$900$		0			0
$901$	−1.75505	−	1.01328i	−0.0584692	−	0.0337572i
$902$	−3.88693	−	18.9320i	−0.129421	−	0.630368i
$903$		0			0
$904$	−34.6506	+	24.0886i	−1.15246	+	0.801174i
$905$	−15.6938	+	27.1824i	−0.521679	+	0.903575i
$906$		0			0
$907$	−28.3744	+	16.3820i	−0.942156	+	0.543954i	−0.890635	−	0.454718i	$-0.849740\pi$
$907$	−28.3744	+	16.3820i	−0.942156	+	0.543954i	−0.0515204	+	0.998672i	$0.516407\pi$
$908$	17.4126	+	2.07500i	0.577856	+	0.0688612i
$909$		0			0
$910$	−12.0376	+	25.9721i	−0.399043	+	0.860968i
$911$	−35.5607			−1.17818			−0.589090	−	0.808067i	$-0.700514\pi$
$911$	−35.5607			−1.17818			−0.589090	+	0.808067i	$0.700514\pi$
$912$		0			0
$913$	34.2636	+	59.3464i	1.13396	+	1.96408i
$914$	−29.5355	−	33.2642i	−0.976949	−	1.10028i
$915$		0			0
$916$	16.3091	+	38.0440i	0.538867	+	1.25701i
$917$	0.369912	−	3.26237i	0.0122156	−	0.107733i
$918$		0			0
$919$	13.7621	−	23.8366i	0.453969	−	0.786297i	−0.544660	−	0.838657i	$-0.683341\pi$
$919$	13.7621	−	23.8366i	0.453969	−	0.786297i	0.998628	+	0.0523606i	$0.0166745\pi$
$920$	−18.0525	+	38.3748i	−0.595174	+	1.26518i
$921$		0			0
$922$	5.85459	+	1.94732i	0.192811	+	0.0641315i
$923$		−	20.6327i		−	0.679135i
$924$		0			0
$925$			1.58065i			0.0519713i
$926$	6.23932	−	18.7585i	0.205037	−	0.616441i
$927$		0			0
$928$	−1.08661	+	31.2847i	−0.0356698	+	1.02697i
$929$	17.4740	−	30.2659i	0.573303	−	0.992991i	−0.422920	−	0.906167i	$-0.638995\pi$
$929$	17.4740	−	30.2659i	0.573303	−	0.992991i	0.996224	−	0.0868237i	$-0.0276717\pi$
$930$		0			0
$931$	18.6387	−	5.72048i	0.610858	−	0.187481i
$932$	10.5303	−	4.51421i	0.344930	−	0.147868i
$933$		0			0
$934$	−17.4895	+	15.5290i	−0.572272	+	0.508126i
$935$	1.28035	+	2.21763i	0.0418719	+	0.0725243i
$936$		0			0
$937$	17.7423			0.579615			0.289807	−	0.957085i	$-0.406409\pi$
$937$	17.7423			0.579615			0.289807	+	0.957085i	$0.406409\pi$
$938$	−39.8580	+	28.0471i	−1.30141	+	0.915771i
$939$		0			0
$940$	−0.396498	−	0.0472493i	−0.0129323	−	0.00154110i
$941$	−19.5486	+	11.2864i	−0.637267	+	0.367926i	−0.783561	−	0.621315i	$-0.786599\pi$
$941$	−19.5486	+	11.2864i	−0.637267	+	0.367926i	0.146294	+	0.989241i	$0.453265\pi$
$942$		0			0
$943$	11.4878	−	19.8974i	0.374093	−	0.647949i
$944$	−12.6087	−	12.0035i	−0.410378	−	0.390680i
$945$		0			0
$946$	60.5545	−	12.4324i	1.96880	−	0.404213i
$947$	−23.6178	−	13.6357i	−0.767474	−	0.443102i	0.0644985	−	0.997918i	$-0.479455\pi$
$947$	−23.6178	−	13.6357i	−0.767474	−	0.443102i	−0.831973	+	0.554816i	$0.812789\pi$
$948$		0			0
$949$	40.0764	−	23.1381i	1.30094	−	0.751096i
$950$	−0.992018	−	0.329959i	−0.0321853	−	0.0107053i
$951$		0			0
$952$	−0.0623377	+	2.14771i	−0.00202038	+	0.0696077i
$953$	5.90986			0.191439			0.0957196	−	0.995408i	$-0.469485\pi$
$953$	5.90986			0.191439			0.0957196	+	0.995408i	$0.469485\pi$
$954$		0			0
$955$	−25.1078	+	14.4960i	−0.812468	+	0.469079i
$956$	3.64595	+	2.72709i	0.117919	+	0.0882005i
$957$		0			0
$958$	−1.64024	+	0.336756i	−0.0529936	+	0.0108801i
$959$	2.50074	−	3.38338i	0.0807531	−	0.109255i
$960$		0			0
$961$	−12.1997	+	21.1305i	−0.393538	+	0.681628i
$962$	−18.6443	−	20.9980i	−0.601116	−	0.677002i
$963$		0			0
$964$	−5.58161	+	46.8387i	−0.179771	+	1.50857i
$965$		−	5.97945i		−	0.192485i
$966$		0			0
$967$	14.0032			0.450312			0.225156	−	0.974323i	$-0.427711\pi$
$967$	14.0032			0.450312			0.225156	+	0.974323i	$0.427711\pi$
$968$	0.973149	+	11.5733i	0.0312782	+	0.371980i
$969$		0			0
$970$	15.6888	−	13.9302i	0.503736	−	0.447271i
$971$	7.91244	+	4.56825i	0.253922	+	0.146602i	0.621559	−	0.783367i	$-0.286500\pi$
$971$	7.91244	+	4.56825i	0.253922	+	0.146602i	−0.367637	+	0.929970i	$0.619833\pi$
$972$		0			0
$973$	−2.49804	+	1.08779i	−0.0800836	+	0.0348729i
$974$	33.3717	−	6.85153i	1.06930	−	0.219537i
$975$		0			0
$976$	6.73701	−	27.8657i	0.215646	−	0.891961i
$977$	10.5767	+	18.3194i	0.338379	+	0.586090i	0.984128	−	0.177460i	$-0.0567880\pi$
$977$	10.5767	+	18.3194i	0.338379	+	0.586090i	−0.645749	+	0.763550i	$0.723455\pi$
$978$		0			0
$979$			66.7881i			2.13456i
$980$	30.2384	+	10.8470i	0.965932	+	0.346495i
$981$		0			0
$982$	24.8218	+	8.25607i	0.792095	+	0.263462i
$983$	23.2004	+	40.1843i	0.739979	+	1.28168i	0.952504	+	0.304525i	$0.0984978\pi$
$983$	23.2004	+	40.1843i	0.739979	+	1.28168i	−0.212526	+	0.977156i	$0.568169\pi$
$984$		0			0
$985$	−0.911867	+	1.57940i	−0.0290545	+	0.0503239i
$986$	0.451900	+	2.20107i	0.0143914	+	0.0700963i
$987$		0			0
$988$	17.0704	−	7.31788i	0.543081	−	0.232813i
$989$	63.6422	+	36.7439i	2.02370	+	1.16839i
$990$		0			0
$991$	−1.29280	−	2.23920i	−0.0410672	−	0.0711305i	0.844761	−	0.535143i	$-0.179742\pi$
$991$	−1.29280	−	2.23920i	−0.0410672	−	0.0711305i	−0.885828	+	0.464013i	$0.846409\pi$
$992$	−19.7738	−	37.1723i	−0.627818	−	1.18022i
$993$		0			0
$994$	−23.0618	+	2.07166i	−0.731476	+	0.0657091i
$995$		−	24.6314i		−	0.780868i
$996$		0			0
$997$	−17.9557	+	10.3667i	−0.568662	+	0.328317i	−0.756615	−	0.653861i	$-0.773148\pi$
$997$	−17.9557	+	10.3667i	−0.568662	+	0.328317i	0.187953	+	0.982178i	$0.439815\pi$
$998$	−12.8258	+	11.3881i	−0.405993	+	0.360485i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.e.37.11		32
3.2	odd	2		168.2.bc.a.37.6	yes	32
4.3	odd	2		2016.2.cr.e.1297.13		32
7.4	even	3	inner	504.2.cj.e.109.12		32
8.3	odd	2		2016.2.cr.e.1297.4		32
8.5	even	2	inner	504.2.cj.e.37.12		32
12.11	even	2		672.2.bk.a.625.10		32
21.2	odd	6		1176.2.c.e.589.15		16
21.5	even	6		1176.2.c.f.589.15		16
21.11	odd	6		168.2.bc.a.109.5	yes	32
24.5	odd	2		168.2.bc.a.37.5	✓	32
24.11	even	2		672.2.bk.a.625.7		32
28.11	odd	6		2016.2.cr.e.1873.4		32
56.11	odd	6		2016.2.cr.e.1873.13		32
56.53	even	6	inner	504.2.cj.e.109.11		32
84.11	even	6		672.2.bk.a.529.7		32
84.23	even	6		4704.2.c.e.2353.15		16
84.47	odd	6		4704.2.c.f.2353.2		16
168.5	even	6		1176.2.c.f.589.16		16
168.11	even	6		672.2.bk.a.529.10		32
168.53	odd	6		168.2.bc.a.109.6	yes	32
168.107	even	6		4704.2.c.e.2353.2		16
168.131	odd	6		4704.2.c.f.2353.15		16
168.149	odd	6		1176.2.c.e.589.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.5	✓	32	24.5	odd	2
168.2.bc.a.37.6	yes	32	3.2	odd	2
168.2.bc.a.109.5	yes	32	21.11	odd	6
168.2.bc.a.109.6	yes	32	168.53	odd	6
504.2.cj.e.37.11		32	1.1	even	1	trivial
504.2.cj.e.37.12		32	8.5	even	2	inner
504.2.cj.e.109.11		32	56.53	even	6	inner
504.2.cj.e.109.12		32	7.4	even	3	inner
672.2.bk.a.529.7		32	84.11	even	6
672.2.bk.a.529.10		32	168.11	even	6
672.2.bk.a.625.7		32	24.11	even	2
672.2.bk.a.625.10		32	12.11	even	2
1176.2.c.e.589.15		16	21.2	odd	6
1176.2.c.e.589.16		16	168.149	odd	6
1176.2.c.f.589.15		16	21.5	even	6
1176.2.c.f.589.16		16	168.5	even	6
2016.2.cr.e.1297.4		32	8.3	odd	2
2016.2.cr.e.1297.13		32	4.3	odd	2
2016.2.cr.e.1873.4		32	28.11	odd	6
2016.2.cr.e.1873.13		32	56.11	odd	6
4704.2.c.e.2353.2		16	168.107	even	6
4704.2.c.e.2353.15		16	84.23	even	6
4704.2.c.f.2353.2		16	84.47	odd	6
4704.2.c.f.2353.15		16	168.131	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.446345 - 1.34193i) q^{2} +(-1.60155 - 1.19793i) q^{4} +(1.98722 + 1.14732i) q^{5} +(-1.05630 - 2.42574i) q^{7} +(-2.32238 + 1.61448i) q^{8} +O(q^{10})\)	\(q+(0.446345 - 1.34193i) q^{2} +(-1.60155 - 1.19793i) q^{4} +(1.98722 + 1.14732i) q^{5} +(-1.05630 - 2.42574i) q^{7} +(-2.32238 + 1.61448i) q^{8} +(2.42662 - 2.15461i) q^{10} +(3.36596 - 1.94334i) q^{11} -3.33413i q^{13} +(-3.72665 + 0.334768i) q^{14} +(1.12994 + 3.83709i) q^{16} +(0.143560 + 0.248654i) q^{17} +(-2.41210 - 1.39263i) q^{19} +(-1.80823 - 4.21805i) q^{20} +(-1.10544 - 5.38428i) q^{22} +(3.26713 - 5.65883i) q^{23} +(0.132707 + 0.229856i) q^{25} +(-4.47417 - 1.48817i) q^{26} +(-1.21414 + 5.15033i) q^{28} +5.53374i q^{29} +(-3.72154 - 6.44589i) q^{31} +(5.65345 + 0.196361i) q^{32} +(0.397754 - 0.0816627i) q^{34} +(0.684001 - 6.03242i) q^{35} +(5.15752 + 2.97769i) q^{37} +(-2.94544 + 2.61528i) q^{38} +(-6.46742 + 0.543818i) q^{40} +3.51617 q^{41} +11.2465i q^{43} +(-7.71873 - 0.919816i) q^{44} +(-6.13549 - 6.91004i) q^{46} +(0.0435037 - 0.0753507i) q^{47} +(-4.76845 + 5.12464i) q^{49} +(0.367684 - 0.0754890i) q^{50} +(-3.99404 + 5.33978i) q^{52} +(-6.11258 + 3.52910i) q^{53} +8.91855 q^{55} +(6.36946 + 3.92811i) q^{56} +(7.42590 + 2.46996i) q^{58} +(-3.76909 + 2.17609i) q^{59} +(-6.20693 - 3.58357i) q^{61} +(-10.3110 + 2.11695i) q^{62} +(2.78689 - 7.49888i) q^{64} +(3.82533 - 6.62566i) q^{65} +(11.2804 - 6.51276i) q^{67} +(0.0679497 - 0.570207i) q^{68} +(-7.78978 - 3.61042i) q^{70} +6.18835 q^{71} +(6.93978 + 12.0201i) q^{73} +(6.29789 - 5.59195i) q^{74} +(2.19484 + 5.11989i) q^{76} +(-8.26950 - 6.11219i) q^{77} +(4.49926 - 7.79295i) q^{79} +(-2.15694 + 8.92156i) q^{80} +(1.56942 - 4.71846i) q^{82} +17.6313i q^{83} +0.658842i q^{85} +(15.0921 + 5.01983i) q^{86} +(-4.67954 + 9.94744i) q^{88} +(-8.59194 + 14.8817i) q^{89} +(-8.08774 + 3.52185i) q^{91} +(-12.0113 + 5.14913i) q^{92} +(-0.0816977 - 0.0920113i) q^{94} +(-3.19559 - 5.53493i) q^{95} +6.46528 q^{97} +(4.74854 + 8.68628i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8}+O(q^{10}) \) 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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