LMFDB - Embedded newform 495.2.n.g.136.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.3
Root			$-0.458960 - 1.41253i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.g.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.392557 + 0.285209i) q^{2} +(-0.545277 - 1.67819i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.500445 - 1.54021i) q^{7} +(0.564470 - 1.73726i) q^{8} +O(q^{10})$	\(q+(0.392557 + 0.285209i) q^{2} +(-0.545277 - 1.67819i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.500445 - 1.54021i) q^{7} +(0.564470 - 1.73726i) q^{8} -0.485227 q^{10} +(-3.27586 + 0.518382i) q^{11} +(-4.01105 - 2.91420i) q^{13} +(0.242829 - 0.747352i) q^{14} +(-2.13804 + 1.55338i) q^{16} +(-2.53923 + 1.84486i) q^{17} +(0.339378 - 1.04450i) q^{19} +(1.42755 + 1.03718i) q^{20} +(-1.43381 - 0.730812i) q^{22} +6.75778 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.743409 - 2.28798i) q^{26} +(-2.31189 + 1.67968i) q^{28} +(-1.09732 - 3.37719i) q^{29} +(-6.90648 - 5.01785i) q^{31} -4.93567 q^{32} -1.52296 q^{34} +(1.31018 + 0.951902i) q^{35} +(-1.65626 - 5.09743i) q^{37} +(0.431126 - 0.313231i) q^{38} +(0.564470 + 1.73726i) q^{40} +(1.64408 - 5.05997i) q^{41} +3.41085 q^{43} +(2.65620 + 5.21486i) q^{44} +(2.65281 + 1.92738i) q^{46} +(-2.04000 + 6.27846i) q^{47} +(3.54132 - 2.57292i) q^{49} +(0.392557 - 0.285209i) q^{50} +(-2.70345 + 8.32036i) q^{52} +(7.86059 + 5.71105i) q^{53} +(2.34553 - 2.34488i) q^{55} -2.95823 q^{56} +(0.532447 - 1.63870i) q^{58} +(-2.22043 - 6.83377i) q^{59} +(5.36780 - 3.89994i) q^{61} +(-1.28005 - 3.93958i) q^{62} +(2.33855 + 1.69906i) q^{64} +4.95793 q^{65} +2.36043 q^{67} +(4.48061 + 3.25536i) q^{68} +(0.242829 + 0.747352i) q^{70} +(-13.4749 + 9.79011i) q^{71} +(2.62525 + 8.07968i) q^{73} +(0.803661 - 2.47341i) q^{74} -1.93792 q^{76} +(2.43781 + 4.78610i) q^{77} +(1.61147 + 1.17080i) q^{79} +(0.816659 - 2.51342i) q^{80} +(2.08855 - 1.51742i) q^{82} +(7.72554 - 5.61293i) q^{83} +(0.969900 - 2.98505i) q^{85} +(1.33895 + 0.972807i) q^{86} +(-0.948562 + 5.98364i) q^{88} +2.65371 q^{89} +(-2.48117 + 7.63626i) q^{91} +(-3.68486 - 11.3408i) q^{92} +(-2.59149 + 1.88283i) q^{94} +(0.339378 + 1.04450i) q^{95} +(11.7501 + 8.53692i) q^{97} +2.12399 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	$ 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 8 * q^10 + 4 * q^11 + 2 * q^13 - 22 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 + 2 * q^20 - 28 * q^22 + 8 * q^23 - 4 * q^25 + 6 * q^26 - 2 * q^28 - 26 * q^29 - 10 * q^31 + 56 * q^32 - 4 * q^34 - 4 * q^35 + 22 * q^37 - 30 * q^38 - 6 * q^40 - 6 * q^41 + 28 * q^43 + 68 * q^44 + 16 * q^46 - 20 * q^47 + 10 * q^49 - 2 * q^50 + 30 * q^52 + 14 * q^53 - 6 * q^55 + 68 * q^56 - 6 * q^58 - 16 * q^59 - 38 * q^61 - 20 * q^62 + 10 * q^64 + 12 * q^65 + 20 * q^67 - 48 * q^68 - 22 * q^70 - 54 * q^71 + 2 * q^73 + 28 * q^74 - 44 * q^76 + 34 * q^77 - 12 * q^79 - 22 * q^80 + 30 * q^82 - 28 * q^83 - 4 * q^85 + 74 * q^86 + 46 * q^88 + 76 * q^89 - 34 * q^91 - 8 * q^92 - 10 * q^94 - 4 * q^95 - 18 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	0.392557	+	0.285209i	0.277580	+	0.201673i	0.717861	−	0.696186i	$-0.245121\pi$
$2$	0.392557	+	0.285209i	0.277580	+	0.201673i	−0.440281	+	0.897860i	$0.645121\pi$
$3$		0			0
$3$		0			0
$4$	−0.545277	−	1.67819i	−0.272639	−	0.839096i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$		0			0
$7$	−0.500445	−	1.54021i	−0.189150	−	0.582145i	0.810845	−	0.585261i	$-0.199008\pi$
$7$	−0.500445	−	1.54021i	−0.189150	−	0.582145i	−0.999995	+	0.00311638i	$0.999008\pi$
$8$	0.564470	−	1.73726i	0.199570	−	0.614214i
$9$		0			0
$10$	−0.485227			−0.153442
$11$	−3.27586	+	0.518382i	−0.987710	+	0.156298i
$11$	−3.27586	+	0.518382i	−0.987710	+	0.156298i
$12$		0			0
$13$	−4.01105	−	2.91420i	−1.11247	−	0.808254i	−0.129415	−	0.991590i	$-0.541310\pi$
$13$	−4.01105	−	2.91420i	−1.11247	−	0.808254i	−0.983050	+	0.183337i	$0.941310\pi$
$14$	0.242829	−	0.747352i	0.0648989	−	0.199738i
$15$		0			0
$16$	−2.13804	+	1.55338i	−0.534510	+	0.388344i
$17$	−2.53923	+	1.84486i	−0.615854	+	0.447444i	−0.851471	−	0.524402i	$-0.824289\pi$
$17$	−2.53923	+	1.84486i	−0.615854	+	0.447444i	0.235617	+	0.971846i	$0.424289\pi$
$18$		0			0
$19$	0.339378	−	1.04450i	0.0778586	−	0.239624i	−0.904550	−	0.426367i	$-0.859793\pi$
$19$	0.339378	−	1.04450i	0.0778586	−	0.239624i	0.982409	+	0.186743i	$0.0597931\pi$
$20$	1.42755	+	1.03718i	0.319211	+	0.231920i
$21$		0			0
$22$	−1.43381	−	0.730812i	−0.305689	−	0.155810i
$23$	6.75778			1.40909			0.704547	−	0.709657i	$-0.251150\pi$
$23$	6.75778			1.40909			0.704547	+	0.709657i	$0.251150\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.743409	−	2.28798i	−0.145795	−	0.448710i
$27$		0			0
$28$	−2.31189	+	1.67968i	−0.436905	+	0.317430i
$29$	−1.09732	−	3.37719i	−0.203766	−	0.627129i	−0.999762	−	0.0218260i	$-0.993052\pi$
$29$	−1.09732	−	3.37719i	−0.203766	−	0.627129i	0.795995	−	0.605303i	$-0.206948\pi$
$30$		0			0
$31$	−6.90648	−	5.01785i	−1.24044	−	0.901232i	−0.242812	−	0.970073i	$-0.578070\pi$
$31$	−6.90648	−	5.01785i	−1.24044	−	0.901232i	−0.997628	+	0.0688408i	$0.978070\pi$
$32$	−4.93567			−0.872511
$33$		0			0
$34$	−1.52296			−0.261186
$35$	1.31018	+	0.951902i	0.221461	+	0.160901i
$36$		0			0
$37$	−1.65626	−	5.09743i	−0.272287	−	0.838013i	−0.989924	−	0.141596i	$-0.954777\pi$
$37$	−1.65626	−	5.09743i	−0.272287	−	0.838013i	0.717638	−	0.696417i	$-0.245223\pi$
$38$	0.431126	−	0.313231i	0.0699378	−	0.0508128i
$39$		0			0
$40$	0.564470	+	1.73726i	0.0892506	+	0.274685i
$41$	1.64408	−	5.05997i	0.256763	−	0.790234i	−0.736715	−	0.676204i	$-0.763624\pi$
$41$	1.64408	−	5.05997i	0.256763	−	0.790234i	0.993477	−	0.114030i	$-0.0363761\pi$
$42$		0			0
$43$	3.41085			0.520150			0.260075	−	0.965588i	$-0.416253\pi$
$43$	3.41085			0.520150			0.260075	+	0.965588i	$0.416253\pi$
$44$	2.65620	+	5.21486i	0.400437	+	0.786170i
$45$		0			0
$46$	2.65281	+	1.92738i	0.391136	+	0.284177i
$47$	−2.04000	+	6.27846i	−0.297564	+	0.915808i	0.684784	+	0.728746i	$0.259896\pi$
$47$	−2.04000	+	6.27846i	−0.297564	+	0.915808i	−0.982348	+	0.187062i	$0.940104\pi$
$48$		0			0
$49$	3.54132	−	2.57292i	0.505902	−	0.367560i
$50$	0.392557	−	0.285209i	0.0555159	−	0.0403347i
$51$		0			0
$52$	−2.70345	+	8.32036i	−0.374901	+	1.15383i
$53$	7.86059	+	5.71105i	1.07973	+	0.784473i	0.977637	−	0.210301i	$-0.0674444\pi$
$53$	7.86059	+	5.71105i	1.07973	+	0.784473i	0.102098	+	0.994774i	$0.467444\pi$
$54$		0			0
$55$	2.34553	−	2.34488i	0.316271	−	0.316184i
$56$	−2.95823			−0.395310
$57$		0			0
$58$	0.532447	−	1.63870i	0.0699138	−	0.215172i
$59$	−2.22043	−	6.83377i	−0.289075	−	0.889681i	−0.985148	−	0.171710i	$-0.945071\pi$
$59$	−2.22043	−	6.83377i	−0.289075	−	0.889681i	0.696073	−	0.717971i	$-0.254929\pi$
$60$		0			0
$61$	5.36780	−	3.89994i	0.687277	−	0.499336i	−0.188487	−	0.982076i	$-0.560358\pi$
$61$	5.36780	−	3.89994i	0.687277	−	0.499336i	0.875764	+	0.482740i	$0.160358\pi$
$62$	−1.28005	−	3.93958i	−0.162566	−	0.500328i
$63$		0			0
$64$	2.33855	+	1.69906i	0.292319	+	0.212382i
$65$	4.95793			0.614956
$66$		0			0
$67$	2.36043			0.288373			0.144186	−	0.989551i	$-0.453944\pi$
$67$	2.36043			0.288373			0.144186	+	0.989551i	$0.453944\pi$
$68$	4.48061	+	3.25536i	0.543354	+	0.394770i
$69$		0			0
$70$	0.242829	+	0.747352i	0.0290237	+	0.0893256i
$71$	−13.4749	+	9.79011i	−1.59918	+	1.16187i	−0.710122	+	0.704078i	$0.751360\pi$
$71$	−13.4749	+	9.79011i	−1.59918	+	1.16187i	−0.889058	+	0.457794i	$0.848640\pi$
$72$		0			0
$73$	2.62525	+	8.07968i	0.307262	+	0.945655i	0.978823	+	0.204706i	$0.0656239\pi$
$73$	2.62525	+	8.07968i	0.307262	+	0.945655i	−0.671562	+	0.740949i	$0.734376\pi$
$74$	0.803661	−	2.47341i	0.0934237	−	0.287528i
$75$		0			0
$76$	−1.93792			−0.222295
$77$	2.43781	+	4.78610i	0.277814	+	0.545426i
$78$		0			0
$79$	1.61147	+	1.17080i	0.181305	+	0.131726i	0.674736	−	0.738059i	$-0.264258\pi$
$79$	1.61147	+	1.17080i	0.181305	+	0.131726i	−0.493431	+	0.869785i	$0.664258\pi$
$80$	0.816659	−	2.51342i	0.0913052	−	0.281009i
$81$		0			0
$82$	2.08855	−	1.51742i	0.230641	−	0.167571i
$83$	7.72554	−	5.61293i	0.847988	−	0.616099i	−0.0766027	−	0.997062i	$-0.524407\pi$
$83$	7.72554	−	5.61293i	0.847988	−	0.616099i	0.924590	+	0.380962i	$0.124407\pi$
$84$		0			0
$85$	0.969900	−	2.98505i	0.105200	−	0.323774i
$86$	1.33895	+	0.972807i	0.144383	+	0.104900i
$87$		0			0
$88$	−0.948562	+	5.98364i	−0.101117	+	0.637858i
$89$	2.65371			0.281293			0.140647	−	0.990060i	$-0.455082\pi$
$89$	2.65371			0.281293			0.140647	+	0.990060i	$0.455082\pi$
$90$		0			0
$91$	−2.48117	+	7.63626i	−0.260097	+	0.800497i
$92$	−3.68486	−	11.3408i	−0.384174	−	1.18236i
$93$		0			0
$94$	−2.59149	+	1.88283i	−0.267292	+	0.194199i
$95$	0.339378	+	1.04450i	0.0348194	+	0.107163i
$96$		0			0
$97$	11.7501	+	8.53692i	1.19304	+	0.866793i	0.993582	−	0.113114i	$-0.0360824\pi$
$97$	11.7501	+	8.53692i	1.19304	+	0.866793i	0.199456	+	0.979907i	$0.436082\pi$
$98$	2.12399			0.214555
$99$		0			0
$100$	−1.76455			−0.176455
$101$	−14.3137	−	10.3995i	−1.42427	−	1.03479i	−0.991048	−	0.133504i	$-0.957377\pi$
$101$	−14.3137	−	10.3995i	−1.42427	−	1.03479i	−0.433220	−	0.901288i	$-0.642623\pi$
$102$		0			0
$103$	−1.52540	−	4.69471i	−0.150303	−	0.462584i	0.847352	−	0.531031i	$-0.178195\pi$
$103$	−1.52540	−	4.69471i	−0.150303	−	0.462584i	−0.997655	+	0.0684477i	$0.978195\pi$
$104$	−7.32684	+	5.32326i	−0.718456	+	0.521989i
$105$		0			0
$106$	1.45688	+	4.48383i	0.141505	+	0.435508i
$107$	3.93919	−	12.1236i	0.380816	−	1.17203i	−0.558655	−	0.829400i	$-0.688682\pi$
$107$	3.93919	−	12.1236i	0.380816	−	1.17203i	0.939470	−	0.342630i	$-0.111318\pi$
$108$		0			0
$109$	15.5953			1.49376			0.746879	−	0.664960i	$-0.231551\pi$
$109$	15.5953			1.49376			0.746879	+	0.664960i	$0.231551\pi$
$110$	1.58954	−	0.251533i	0.151556	−	0.0239827i
$111$		0			0
$112$	3.46250	+	2.51565i	0.327175	+	0.237707i
$113$	−1.74092	+	5.35799i	−0.163772	+	0.504038i	−0.998944	−	0.0459513i	$-0.985368\pi$
$113$	−1.74092	+	5.35799i	−0.163772	+	0.504038i	0.835172	+	0.549989i	$0.185368\pi$
$114$		0			0
$115$	−5.46716	+	3.97212i	−0.509815	+	0.370402i
$116$	−5.06923	+	3.68301i	−0.470666	+	0.341959i
$117$		0			0
$118$	1.07741	−	3.31593i	0.0991837	−	0.305256i
$119$	4.11222	+	2.98770i	0.376966	+	0.273882i
$120$		0			0
$121$	10.4626	−	3.39630i	0.951142	−	0.308755i
$122$	3.21947			0.291477
$123$		0			0
$124$	−4.65497	+	14.3265i	−0.418028	+	1.28656i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$		0			0
$127$	−5.95671	+	4.32780i	−0.528572	+	0.384030i	−0.819823	−	0.572616i	$-0.805928\pi$
$127$	−5.95671	+	4.32780i	−0.528572	+	0.384030i	0.291251	+	0.956647i	$0.405928\pi$
$128$	3.48384	+	10.7221i	0.307931	+	0.947713i
$129$		0			0
$130$	1.94627	+	1.41405i	0.170699	+	0.124020i
$131$	−6.74024			−0.588897			−0.294449	−	0.955667i	$-0.595136\pi$
$131$	−6.74024			−0.588897			−0.294449	+	0.955667i	$0.595136\pi$
$132$		0			0
$133$	−1.77859			−0.154223
$134$	0.926604	+	0.673217i	0.0800464	+	0.0581571i
$135$		0			0
$136$	1.77168	+	5.45268i	0.151920	+	0.467563i
$137$	−5.11301	+	3.71482i	−0.436834	+	0.317379i	−0.784376	−	0.620286i	$-0.787017\pi$
$137$	−5.11301	+	3.71482i	−0.436834	+	0.317379i	0.347542	+	0.937665i	$0.387017\pi$
$138$		0			0
$139$	−4.35212	−	13.3945i	−0.369142	−	1.13610i	−0.947346	−	0.320211i	$-0.896246\pi$
$139$	−4.35212	−	13.3945i	−0.369142	−	1.13610i	0.578204	−	0.815892i	$-0.303754\pi$
$140$	0.883062	−	2.71779i	0.0746324	−	0.229695i
$141$		0			0
$142$	−8.08191			−0.678219
$143$	14.6503	+	7.46726i	1.22512	+	0.624444i
$144$		0			0
$145$	2.87281	+	2.08722i	0.238574	+	0.173334i
$146$	−1.27384	+	3.92048i	−0.105424	+	0.324461i
$147$		0			0
$148$	−7.65135	+	5.55903i	−0.628937	+	0.456950i
$149$	−14.0344	+	10.1966i	−1.14975	+	0.835340i	−0.988447	−	0.151566i	$-0.951568\pi$
$149$	−14.0344	+	10.1966i	−1.14975	+	0.835340i	−0.161299	+	0.986906i	$0.551568\pi$
$150$		0			0
$151$	−2.78565	+	8.57334i	−0.226693	+	0.697689i	0.771423	+	0.636323i	$0.219546\pi$
$151$	−2.78565	+	8.57334i	−0.226693	+	0.697689i	−0.998115	+	0.0613655i	$0.980454\pi$
$152$	−1.62300	−	1.17918i	−0.131642	−	0.0956438i
$153$		0			0
$154$	−0.408062	+	2.57410i	−0.0328825	+	0.207427i
$155$	8.53688			0.685698
$156$		0			0
$157$	3.68855	−	11.3522i	0.294378	−	0.906003i	−0.689051	−	0.724713i	$-0.741972\pi$
$157$	3.68855	−	11.3522i	0.294378	−	0.906003i	0.983430	−	0.181291i	$-0.0580275\pi$
$158$	0.298671	+	0.919214i	0.0237610	+	0.0731287i
$159$		0			0
$160$	3.99304	−	2.90111i	0.315677	−	0.229353i
$161$	−3.38189	−	10.4084i	−0.266531	−	0.820297i
$162$		0			0
$163$	1.88293	+	1.36803i	0.147482	+	0.107152i	0.659080	−	0.752073i	$-0.270946\pi$
$163$	1.88293	+	1.36803i	0.147482	+	0.107152i	−0.511597	+	0.859225i	$0.670946\pi$
$164$	−9.38807			−0.733085
$165$		0			0
$166$	4.63357			0.359635
$167$	−7.94813	−	5.77465i	−0.615044	−	0.446856i	0.236143	−	0.971718i	$-0.424117\pi$
$167$	−7.94813	−	5.77465i	−0.615044	−	0.446856i	−0.851187	+	0.524862i	$0.824117\pi$
$168$		0			0
$169$	3.57876	+	11.0143i	0.275289	+	0.847252i
$170$	1.23210	−	0.895176i	0.0944981	−	0.0686569i
$171$		0			0
$172$	−1.85986	−	5.72406i	−0.141813	−	0.436456i
$173$	7.18156	−	22.1026i	0.546004	−	1.68043i	−0.172588	−	0.984994i	$-0.555213\pi$
$173$	7.18156	−	22.1026i	0.546004	−	1.68043i	0.718592	−	0.695432i	$-0.244787\pi$
$174$		0			0
$175$	−1.61947			−0.122421
$176$	6.19868	−	6.19697i	0.467243	−	0.467114i
$177$		0			0
$178$	1.04173	+	0.756864i	0.0780812	+	0.0567293i
$179$	−0.116360	+	0.358121i	−0.00869719	+	0.0267672i	−0.955311	−	0.295603i	$-0.904480\pi$
$179$	−0.116360	+	0.358121i	−0.00869719	+	0.0267672i	0.946614	+	0.322370i	$0.104480\pi$
$180$		0			0
$181$	6.13362	−	4.45634i	0.455909	−	0.331237i	−0.336016	−	0.941856i	$-0.609079\pi$
$181$	6.13362	−	4.45634i	0.455909	−	0.331237i	0.791924	+	0.610619i	$0.209079\pi$
$182$	−3.15193	+	2.29001i	−0.233637	+	0.169747i
$183$		0			0
$184$	3.81456	−	11.7400i	0.281213	−	0.865486i
$185$	4.33614	+	3.15039i	0.318799	+	0.231621i
$186$		0			0
$187$	7.36183	−	7.35980i	0.538351	−	0.538202i
$188$	11.6488			0.849578
$189$		0			0
$190$	−0.164675	+	0.506819i	−0.0119468	+	0.0367685i
$191$	0.668717	+	2.05810i	0.0483867	+	0.148919i	0.972331	−	0.233609i	$-0.0750536\pi$
$191$	0.668717	+	2.05810i	0.0483867	+	0.148919i	−0.923944	+	0.382528i	$0.875054\pi$
$192$		0			0
$193$	15.0381	−	10.9258i	1.08246	−	0.786455i	0.104352	−	0.994540i	$-0.466723\pi$
$193$	15.0381	−	10.9258i	1.08246	−	0.786455i	0.978111	+	0.208085i	$0.0667230\pi$
$194$	2.17776	+	6.70246i	0.156354	+	0.481208i
$195$		0			0
$196$	−6.24885	−	4.54005i	−0.446346	−	0.324289i
$197$	−8.70640			−0.620306			−0.310153	−	0.950687i	$-0.600380\pi$
$197$	−8.70640			−0.620306			−0.310153	+	0.950687i	$0.600380\pi$
$198$		0			0
$199$	−18.9231			−1.34142			−0.670712	−	0.741718i	$-0.734011\pi$
$199$	−18.9231			−1.34142			−0.670712	+	0.741718i	$0.734011\pi$
$200$	−1.47780	−	1.07369i	−0.104496	−	0.0759211i
$201$		0			0
$202$	−2.65291	−	8.16481i	−0.186658	−	0.574474i
$203$	−4.65244	+	3.38020i	−0.326537	+	0.237243i
$204$		0			0
$205$	1.64408	+	5.05997i	0.114828	+	0.353403i
$206$	0.740168	−	2.27800i	0.0515699	−	0.158716i
$207$		0			0
$208$	13.1026			0.908505
$209$	−0.570306	+	3.59756i	−0.0394489	+	0.248848i
$210$		0			0
$211$	−14.0382	−	10.1994i	−0.966431	−	0.702153i	−0.0117958	−	0.999930i	$-0.503755\pi$
$211$	−14.0382	−	10.1994i	−0.966431	−	0.702153i	−0.954635	+	0.297777i	$0.903755\pi$
$212$	5.29804	−	16.3057i	0.363871	−	1.11988i
$213$		0			0
$214$	5.00411	−	3.63570i	0.342074	−	0.248531i
$215$	−2.75944	+	2.00485i	−0.188192	+	0.136730i
$216$		0			0
$217$	−4.27223	+	13.1486i	−0.290018	+	0.892584i
$218$	6.12204	+	4.44792i	0.414637	+	0.301251i
$219$		0			0
$220$	−5.21413	−	2.65764i	−0.351537	−	0.179178i
$221$	15.5613			1.04677
$222$		0			0
$223$	2.22209	−	6.83888i	0.148802	−	0.457965i	−0.848678	−	0.528909i	$-0.822601\pi$
$223$	2.22209	−	6.83888i	0.148802	−	0.457965i	0.997480	+	0.0709441i	$0.0226012\pi$
$224$	2.47003	+	7.60197i	0.165036	+	0.507928i
$225$		0			0
$226$	−2.21156	+	1.60679i	−0.147111	+	0.106882i
$227$	8.43654	+	25.9650i	0.559953	+	1.72336i	0.682491	+	0.730894i	$0.260897\pi$
$227$	8.43654	+	25.9650i	0.559953	+	1.72336i	−0.122538	+	0.992464i	$0.539103\pi$
$228$		0			0
$229$	−10.0126	−	7.27460i	−0.661653	−	0.480719i	0.205568	−	0.978643i	$-0.434096\pi$
$229$	−10.0126	−	7.27460i	−0.661653	−	0.480719i	−0.867221	+	0.497924i	$0.834096\pi$
$230$	−3.27906			−0.216215
$231$		0			0
$232$	−6.48646			−0.425857
$233$	−11.7669	−	8.54918i	−0.770878	−	0.560075i	0.131350	−	0.991336i	$-0.458069\pi$
$233$	−11.7669	−	8.54918i	−0.770878	−	0.560075i	−0.902227	+	0.431261i	$0.858069\pi$
$234$		0			0
$235$	−2.04000	−	6.27846i	−0.133075	−	0.409562i
$236$	−10.2576	+	7.45260i	−0.667715	+	0.485123i
$237$		0			0
$238$	0.762160	+	2.34569i	0.0494035	+	0.152048i
$239$	8.93886	−	27.5110i	0.578207	−	1.77954i	−0.0467845	−	0.998905i	$-0.514897\pi$
$239$	8.93886	−	27.5110i	0.578207	−	1.77954i	0.624991	−	0.780632i	$-0.285103\pi$
$240$		0			0
$241$	−9.40610			−0.605900			−0.302950	−	0.953006i	$-0.597972\pi$
$241$	−9.40610			−0.605900			−0.302950	+	0.953006i	$0.597972\pi$
$242$	5.07581	+	1.65078i	0.326285	+	0.106116i
$243$		0			0
$244$	−9.47178	−	6.88165i	−0.606369	−	0.440553i
$245$	−1.35266	+	4.16307i	−0.0864184	+	0.265969i
$246$		0			0
$247$	−4.40514	+	3.20052i	−0.280292	+	0.203644i
$248$	−12.6158	+	9.16593i	−0.801105	+	0.582037i
$249$		0			0
$250$	−0.149943	+	0.461478i	−0.00948325	+	0.0291865i
$251$	−0.0263240	−	0.0191255i	−0.00166155	−	0.00120719i	0.586954	−	0.809620i	$-0.300327\pi$
$251$	−0.0263240	−	0.0191255i	−0.00166155	−	0.00120719i	−0.588616	+	0.808413i	$0.700327\pi$
$252$		0			0
$253$	−22.1376	+	3.50311i	−1.39178	+	0.220239i
$254$	−3.57267			−0.224170
$255$		0			0
$256$	0.0960403	−	0.295582i	0.00600252	−	0.0184738i
$257$	2.04470	+	6.29295i	0.127545	+	0.392544i	0.994356	−	0.106093i	$-0.0338342\pi$
$257$	2.04470	+	6.29295i	0.127545	+	0.392544i	−0.866811	+	0.498637i	$0.833834\pi$
$258$		0			0
$259$	−7.02226	+	5.10197i	−0.436342	+	0.317021i
$260$	−2.70345	−	8.32036i	−0.167661	−	0.516007i
$261$		0			0
$262$	−2.64593	−	1.92238i	−0.163466	−	0.118765i
$263$	5.19057			0.320064			0.160032	−	0.987112i	$-0.448840\pi$
$263$	5.19057			0.320064			0.160032	+	0.987112i	$0.448840\pi$
$264$		0			0
$265$	−9.71622			−0.596863
$266$	−0.698196	−	0.507269i	−0.0428092	−	0.0311027i
$267$		0			0
$268$	−1.28709	−	3.96126i	−0.0786215	−	0.241972i
$269$	12.8451	−	9.33248i	0.783177	−	0.569011i	−0.122754	−	0.992437i	$-0.539173\pi$
$269$	12.8451	−	9.33248i	0.783177	−	0.569011i	0.905931	+	0.423426i	$0.139173\pi$
$270$		0			0
$271$	−8.10665	−	24.9497i	−0.492444	−	1.51559i	−0.820903	−	0.571068i	$-0.806529\pi$
$271$	−8.10665	−	24.9497i	−0.492444	−	1.51559i	0.328459	−	0.944518i	$-0.393471\pi$
$272$	2.56322	−	7.88877i	0.155418	−	0.478327i
$273$		0			0
$274$	−3.06665			−0.185263
$275$	−0.519286	+	3.27572i	−0.0313141	+	0.197533i
$276$		0			0
$277$	5.26762	+	3.82715i	0.316501	+	0.229951i	0.734681	−	0.678413i	$-0.237332\pi$
$277$	5.26762	+	3.82715i	0.316501	+	0.229951i	−0.418180	+	0.908364i	$0.637332\pi$
$278$	2.11177	−	6.49935i	0.126655	−	0.389805i
$279$		0			0
$280$	2.39326	−	1.73881i	0.143025	−	0.103914i
$281$	−9.07621	+	6.59425i	−0.541441	+	0.393380i	−0.824620	−	0.565687i	$-0.808611\pi$
$281$	−9.07621	+	6.59425i	−0.541441	+	0.393380i	0.283179	+	0.959067i	$0.408611\pi$
$282$		0			0
$283$	2.55759	−	7.87145i	0.152033	−	0.467909i	−0.845815	−	0.533476i	$-0.820886\pi$
$283$	2.55759	−	7.87145i	0.152033	−	0.467909i	0.997848	+	0.0655669i	$0.0208856\pi$
$284$	23.7773	+	17.2752i	1.41092	+	1.02509i
$285$		0			0
$286$	3.62136	+	7.10973i	0.214135	+	0.420407i
$287$	−8.61619			−0.508597
$288$		0			0
$289$	−2.20910	+	6.79890i	−0.129947	+	0.399935i
$290$	0.532447	+	1.63870i	0.0312664	+	0.0962281i
$291$		0			0
$292$	12.1278	−	8.81133i	0.709723	−	0.515644i
$293$	−0.129311	−	0.397978i	−0.00755443	−	0.0232501i	0.947208	−	0.320619i	$-0.103891\pi$
$293$	−0.129311	−	0.397978i	−0.00755443	−	0.0232501i	−0.954763	+	0.297369i	$0.903891\pi$
$294$		0			0
$295$	5.81315	+	4.22350i	0.338455	+	0.245902i
$296$	−9.79048			−0.569060
$297$		0			0
$298$	−8.41749			−0.487612
$299$	−27.1058	−	19.6935i	−1.56757	−	1.13891i
$300$		0			0
$301$	−1.70694	−	5.25343i	−0.0983866	−	0.302803i
$302$	−3.53872	+	2.57103i	−0.203631	+	0.147946i
$303$		0			0
$304$	0.896895	+	2.76036i	0.0514405	+	0.158318i
$305$	−2.05032	+	6.31023i	−0.117401	+	0.361323i
$306$		0			0
$307$	−32.7941			−1.87166			−0.935828	−	0.352457i	$-0.885346\pi$
$307$	−32.7941			−1.87166			−0.935828	+	0.352457i	$0.885346\pi$
$308$	6.70270	−	6.70086i	0.381922	−	0.381817i
$309$		0			0
$310$	3.35121	+	2.43480i	0.190336	+	0.138287i
$311$	−0.157476	+	0.484661i	−0.00892963	+	0.0274826i	−0.955422	−	0.295243i	$-0.904599\pi$
$311$	−0.157476	+	0.484661i	−0.00892963	+	0.0274826i	0.946492	+	0.322726i	$0.104599\pi$
$312$		0			0
$313$	−2.29169	+	1.66501i	−0.129534	+	0.0941118i	−0.650666	−	0.759364i	$-0.725510\pi$
$313$	−2.29169	+	1.66501i	−0.129534	+	0.0941118i	0.521132	+	0.853476i	$0.325510\pi$
$314$	4.68572	−	3.40437i	0.264430	−	0.192120i
$315$		0			0
$316$	1.08613	−	3.34277i	0.0610997	−	0.188046i
$317$	21.8364	+	15.8651i	1.22646	+	0.891073i	0.996619	−	0.0821562i	$-0.0261807\pi$
$317$	21.8364	+	15.8651i	1.22646	+	0.891073i	0.229837	+	0.973229i	$0.426181\pi$
$318$		0			0
$319$	5.34533	+	10.4944i	0.299281	+	0.587573i
$320$	−2.89061			−0.161590
$321$		0			0
$322$	1.64099	−	5.05044i	0.0914486	−	0.281450i
$323$	1.06519	+	3.27833i	0.0592689	+	0.182411i
$324$		0			0
$325$	−4.01105	+	2.91420i	−0.222493	+	0.161651i
$326$	0.348983	+	1.07406i	0.0193284	+	0.0594866i
$327$		0			0
$328$	−7.86244	−	5.71240i	−0.434131	−	0.315415i
$329$	10.6911			0.589417
$330$		0			0
$331$	21.5474			1.18435			0.592175	−	0.805809i	$-0.298269\pi$
$331$	21.5474			1.18435			0.592175	+	0.805809i	$0.298269\pi$
$332$	−13.6321	−	9.90432i	−0.748160	−	0.543570i
$333$		0			0
$334$	−1.47311	−	4.53376i	−0.0806049	−	0.248076i
$335$	−1.90963	+	1.38743i	−0.104334	+	0.0758032i
$336$		0			0
$337$	3.39195	+	10.4393i	0.184771	+	0.568667i	0.999944	−	0.0105503i	$-0.00335833\pi$
$337$	3.39195	+	10.4393i	0.184771	+	0.568667i	−0.815173	+	0.579217i	$0.803358\pi$
$338$	−1.73651	+	5.34443i	−0.0944536	+	0.290698i
$339$		0			0
$340$	−5.53834			−0.300359
$341$	25.2258	+	12.8576i	1.36606	+	0.696278i
$342$		0			0
$343$	−14.9063	−	10.8301i	−0.804866	−	0.584770i
$344$	1.92532	−	5.92554i	0.103807	−	0.319484i
$345$		0			0
$346$	9.12302	−	6.62826i	0.490457	−	0.356338i
$347$	−13.5261	+	9.82728i	−0.726119	+	0.527556i	−0.888333	−	0.459199i	$-0.848136\pi$
$347$	−13.5261	+	9.82728i	−0.726119	+	0.527556i	0.162215	+	0.986756i	$0.448136\pi$
$348$		0			0
$349$	1.42097	−	4.37331i	0.0760629	−	0.234098i	−0.905795	−	0.423717i	$-0.860725\pi$
$349$	1.42097	−	4.37331i	0.0760629	−	0.234098i	0.981858	+	0.189619i	$0.0607253\pi$
$350$	−0.635735	−	0.461889i	−0.0339815	−	0.0246890i
$351$		0			0
$352$	16.1686	−	2.55856i	0.861788	−	0.136372i
$353$	−14.4628			−0.769775			−0.384887	−	0.922964i	$-0.625760\pi$
$353$	−14.4628			−0.769775			−0.384887	+	0.922964i	$0.625760\pi$
$354$		0			0
$355$	5.14697	−	15.8407i	0.273173	−	0.840739i
$356$	−1.44701	−	4.45344i	−0.0766914	−	0.236032i
$357$		0			0
$358$	−0.147817	+	0.107396i	−0.00781240	+	0.00567604i
$359$	−2.64715	−	8.14708i	−0.139711	−	0.429986i	0.856582	−	0.516011i	$-0.172584\pi$
$359$	−2.64715	−	8.14708i	−0.139711	−	0.429986i	−0.996293	+	0.0860247i	$0.972584\pi$
$360$		0			0
$361$	14.3955	+	10.4590i	0.757659	+	0.550472i
$362$	3.67879			0.193353
$363$		0			0
$364$	14.1680			0.742607
$365$	−6.87299	−	4.99352i	−0.359749	−	0.261373i
$366$		0			0
$367$	0.355143	+	1.09302i	0.0185383	+	0.0570551i	0.959898	−	0.280350i	$-0.0904507\pi$
$367$	0.355143	+	1.09302i	0.0185383	+	0.0570551i	−0.941359	+	0.337405i	$0.890451\pi$
$368$	−14.4484	+	10.4974i	−0.753175	+	0.547214i
$369$		0			0
$370$	0.803661	+	2.47341i	0.0417803	+	0.128587i
$371$	4.86243	−	14.9650i	0.252445	−	0.776945i
$372$		0			0
$373$	32.1348			1.66388			0.831939	−	0.554867i	$-0.187231\pi$
$373$	32.1348			1.66388			0.831939	+	0.554867i	$0.187231\pi$
$374$	4.98902	−	0.789478i	0.257976	−	0.0408229i
$375$		0			0
$376$	9.75581	+	7.08801i	0.503117	+	0.365536i
$377$	−5.44042	+	16.7439i	−0.280196	+	0.862354i
$378$		0			0
$379$	−11.9238	+	8.66316i	−0.612485	+	0.444996i	−0.850289	−	0.526317i	$-0.823573\pi$
$379$	−11.9238	+	8.66316i	−0.612485	+	0.444996i	0.237803	+	0.971313i	$0.423573\pi$
$380$	1.56781	−	1.13908i	0.0804271	−	0.0584337i
$381$		0			0
$382$	−0.324480	+	0.998646i	−0.0166018	+	0.0510952i
$383$	−24.3423	−	17.6857i	−1.24383	−	0.903698i	−0.245986	−	0.969273i	$-0.579112\pi$
$383$	−24.3423	−	17.6857i	−1.24383	−	0.903698i	−0.997848	+	0.0655753i	$0.979112\pi$
$384$		0			0
$385$	−4.78542	−	2.43913i	−0.243888	−	0.124309i
$386$	9.01943			0.459077
$387$		0			0
$388$	7.91954	−	24.3738i	0.402054	−	1.23739i
$389$	−10.7154	−	32.9785i	−0.543291	−	1.67208i	−0.725018	−	0.688730i	$-0.758169\pi$
$389$	−10.7154	−	32.9785i	−0.543291	−	1.67208i	0.181727	−	0.983349i	$-0.441831\pi$
$390$		0			0
$391$	−17.1596	+	12.4672i	−0.867797	+	0.630491i
$392$	−2.47086	−	7.60452i	−0.124797	−	0.384086i
$393$		0			0
$394$	−3.41776	−	2.48315i	−0.172184	−	0.125099i
$395$	−1.99189			−0.100223
$396$		0			0
$397$	36.4341			1.82858			0.914288	−	0.405064i	$-0.132751\pi$
$397$	36.4341			1.82858			0.914288	+	0.405064i	$0.132751\pi$
$398$	−7.42840	−	5.39705i	−0.372352	−	0.270529i
$399$		0			0
$400$	0.816659	+	2.51342i	0.0408329	+	0.125671i
$401$	17.4291	−	12.6630i	0.870367	−	0.632359i	−0.0603183	−	0.998179i	$-0.519212\pi$
$401$	17.4291	−	12.6630i	0.870367	−	0.632359i	0.930685	+	0.365820i	$0.119212\pi$
$402$		0			0
$403$	13.0792	+	40.2537i	0.651523	+	2.00518i
$404$	−9.64745	+	29.6918i	−0.479979	+	1.47722i
$405$		0			0
$406$	−2.79041			−0.138486
$407$	8.06809	+	15.8399i	0.399920	+	0.785156i
$408$		0			0
$409$	4.67164	+	3.39415i	0.230998	+	0.167830i	0.697263	−	0.716815i	$-0.254401\pi$
$409$	4.67164	+	3.39415i	0.230998	+	0.167830i	−0.466265	+	0.884645i	$0.654401\pi$
$410$	−0.797753	+	2.45523i	−0.0393982	+	0.121255i
$411$		0			0
$412$	−7.04686	+	5.11984i	−0.347174	+	0.252236i
$413$	−9.41424	+	6.83985i	−0.463245	+	0.336567i
$414$		0			0
$415$	−2.95089	+	9.08191i	−0.144854	+	0.445814i
$416$	19.7972	+	14.3835i	0.970638	+	0.705210i
$417$		0			0
$418$	−1.24994	+	1.24959i	−0.0611363	+	0.0611195i
$419$	13.4745			0.658273			0.329137	−	0.944282i	$-0.393242\pi$
$419$	13.4745			0.658273			0.329137	+	0.944282i	$0.393242\pi$
$420$		0			0
$421$	−7.48952	+	23.0504i	−0.365017	+	1.12341i	0.584954	+	0.811067i	$0.301113\pi$
$421$	−7.48952	+	23.0504i	−0.365017	+	1.12341i	−0.949971	+	0.312340i	$0.898887\pi$
$422$	−2.60185	−	8.00766i	−0.126656	−	0.389807i
$423$		0			0
$424$	14.3587	−	10.4322i	0.697318	−	0.506631i
$425$	0.969900	+	2.98505i	0.0470471	+	0.144796i
$426$		0			0
$427$	−8.69301	−	6.31584i	−0.420684	−	0.305645i
$428$	−22.4936			−1.08727
$429$		0			0
$430$	−1.65504			−0.0798130
$431$	−0.627719	−	0.456065i	−0.0302362	−	0.0219679i	0.572565	−	0.819860i	$-0.305949\pi$
$431$	−0.627719	−	0.456065i	−0.0302362	−	0.0219679i	−0.602801	+	0.797892i	$0.705949\pi$
$432$		0			0
$433$	10.6870	+	32.8911i	0.513583	+	1.58065i	0.785845	+	0.618423i	$0.212228\pi$
$433$	10.6870	+	32.8911i	0.513583	+	1.58065i	−0.272262	+	0.962223i	$0.587772\pi$
$434$	−5.42719	+	3.94309i	−0.260514	+	0.189274i
$435$		0			0
$436$	−8.50376	−	26.1719i	−0.407256	−	1.25341i
$437$	2.29344	−	7.05849i	0.109710	−	0.337653i
$438$		0			0
$439$	7.24100			0.345594			0.172797	−	0.984957i	$-0.444720\pi$
$439$	7.24100			0.345594			0.172797	+	0.984957i	$0.444720\pi$
$440$	−2.74969	−	5.39842i	−0.131086	−	0.257359i
$441$		0			0
$442$	6.10869	+	4.43822i	0.290561	+	0.211105i
$443$	1.67245	−	5.14726i	0.0794603	−	0.244554i	−0.903433	−	0.428729i	$-0.858961\pi$
$443$	1.67245	−	5.14726i	0.0794603	−	0.244554i	0.982893	+	0.184175i	$0.0589615\pi$
$444$		0			0
$445$	−2.14690	+	1.55981i	−0.101773	+	0.0739423i
$446$	2.82281	−	2.05089i	0.133664	−	0.0971124i
$447$		0			0
$448$	1.44659	−	4.45214i	0.0683449	−	0.210344i
$449$	10.4290	+	7.57708i	0.492173	+	0.357585i	0.806019	−	0.591889i	$-0.201618\pi$
$449$	10.4290	+	7.57708i	0.492173	+	0.357585i	−0.313846	+	0.949474i	$0.601618\pi$
$450$		0			0
$451$	−2.76279	+	17.4280i	−0.130095	+	0.820654i
$452$	9.94102			0.467586
$453$		0			0
$454$	−4.09364	+	12.5989i	−0.192124	+	0.591297i
$455$	−2.48117	−	7.63626i	−0.116319	−	0.357993i
$456$		0			0
$457$	−1.37974	+	1.00244i	−0.0645415	+	0.0468921i	−0.619588	−	0.784927i	$-0.712700\pi$
$457$	−1.37974	+	1.00244i	−0.0645415	+	0.0468921i	0.555047	+	0.831819i	$0.312700\pi$
$458$	−1.85574	−	5.71139i	−0.0867132	−	0.266876i
$459$		0			0
$460$	9.64710	+	7.00903i	0.449798	+	0.326798i
$461$	29.9226			1.39364			0.696818	−	0.717248i	$-0.254599\pi$
$461$	29.9226			1.39364			0.696818	+	0.717248i	$0.254599\pi$
$462$		0			0
$463$	−33.9765			−1.57902			−0.789511	−	0.613736i	$-0.789666\pi$
$463$	−33.9765			−1.57902			−0.789511	+	0.613736i	$0.789666\pi$
$464$	7.59216	+	5.51603i	0.352457	+	0.256075i
$465$		0			0
$466$	−2.18089	−	6.71208i	−0.101028	−	0.310931i
$467$	−0.137470	+	0.0998775i	−0.00636133	+	0.00462178i	−0.590961	−	0.806700i	$-0.701251\pi$
$467$	−0.137470	+	0.0998775i	−0.00636133	+	0.00462178i	0.584600	+	0.811322i	$0.301251\pi$
$468$		0			0
$469$	−1.18127	−	3.63556i	−0.0545458	−	0.167875i
$470$	0.989861	−	3.04648i	0.0456589	−	0.140524i
$471$		0			0
$472$	−13.1254			−0.604146
$473$	−11.1735	+	1.76813i	−0.513757	+	0.0812985i
$474$		0			0
$475$	−0.888503	−	0.645535i	−0.0407673	−	0.0296192i
$476$	2.77163	−	8.53022i	0.127038	−	0.390982i
$477$		0			0
$478$	11.3554	−	8.25018i	0.519384	−	0.377354i
$479$	−11.8262	+	8.59223i	−0.540352	+	0.392589i	−0.824216	−	0.566276i	$-0.808384\pi$
$479$	−11.8262	+	8.59223i	−0.540352	+	0.392589i	0.283863	+	0.958865i	$0.408384\pi$
$480$		0			0
$481$	−8.21161	+	25.2727i	−0.374417	+	1.15234i
$482$	−3.69243	−	2.68271i	−0.168186	−	0.122194i
$483$		0			0
$484$	−11.4046	−	15.7062i	−0.518393	−	0.713920i
$485$	−14.5239			−0.659495
$486$		0			0
$487$	−7.40157	+	22.7797i	−0.335397	+	1.03225i	0.631129	+	0.775678i	$0.282592\pi$
$487$	−7.40157	+	22.7797i	−0.335397	+	1.03225i	−0.966526	+	0.256569i	$0.917408\pi$
$488$	−3.74524	−	11.5267i	−0.169539	−	0.521788i
$489$		0			0
$490$	−1.71834	+	1.24845i	−0.0776268	+	0.0563992i
$491$	9.80474	+	30.1759i	0.442482	+	1.36182i	0.885222	+	0.465169i	$0.154006\pi$
$491$	9.80474	+	30.1759i	0.442482	+	1.36182i	−0.442740	+	0.896650i	$0.645994\pi$
$492$		0			0
$493$	9.01679	+	6.55108i	0.406096	+	0.295046i
$494$	−2.64209			−0.118873
$495$		0			0
$496$	22.5609			1.01302
$497$	21.8223	+	15.8548i	0.978864	+	0.711186i
$498$		0			0
$499$	10.2290	+	31.4816i	0.457912	+	1.40931i	0.867682	+	0.497119i	$0.165609\pi$
$499$	10.2290	+	31.4816i	0.457912	+	1.40931i	−0.409770	+	0.912189i	$0.634391\pi$
$500$	1.42755	−	1.03718i	0.0638422	−	0.0463841i
$501$		0			0
$502$	−0.00487889	−	0.0150157i	−0.000217755	−	0.000670182i
$503$	5.60622	−	17.2542i	0.249969	−	0.769326i	−0.744810	−	0.667276i	$-0.767460\pi$
$503$	5.60622	−	17.2542i	0.249969	−	0.769326i	0.994779	−	0.102050i	$-0.0325400\pi$
$504$		0			0
$505$	17.6927			0.787316
$506$	−9.68937	−	4.93867i	−0.430745	−	0.219550i
$507$		0			0
$508$	10.5109	+	7.63664i	0.466347	+	0.338821i
$509$	−5.15242	+	15.8575i	−0.228377	+	0.702872i	0.769554	+	0.638582i	$0.220478\pi$
$509$	−5.15242	+	15.8575i	−0.228377	+	0.702872i	−0.997931	+	0.0642907i	$0.979522\pi$
$510$		0			0
$511$	11.1306	−	8.08687i	0.492389	−	0.357742i
$512$	18.3636	−	13.3419i	0.811565	−	0.589636i
$513$		0			0
$514$	−0.992146	+	3.05351i	−0.0437617	+	0.134685i
$515$	3.99356	+	2.90149i	0.175977	+	0.127855i
$516$		0			0
$517$	3.42810	−	21.6249i	0.150768	−	0.951061i
$518$	−4.21176			−0.185054
$519$		0			0
$520$	2.79861	−	8.61322i	0.122727	−	0.377715i
$521$	6.34181	+	19.5181i	0.277840	+	0.855103i	0.988454	+	0.151521i	$0.0484172\pi$
$521$	6.34181	+	19.5181i	0.277840	+	0.855103i	−0.710614	+	0.703582i	$0.751583\pi$
$522$		0			0
$523$	−0.327380	+	0.237856i	−0.0143153	+	0.0104007i	−0.594920	−	0.803785i	$-0.702816\pi$
$523$	−0.327380	+	0.237856i	−0.0143153	+	0.0104007i	0.580605	+	0.814186i	$0.302816\pi$
$524$	3.67530	+	11.3114i	0.160556	+	0.494141i
$525$		0			0
$526$	2.03759	+	1.48040i	0.0888433	+	0.0645484i
$527$	26.7944			1.16718
$528$		0			0
$529$	22.6676			0.985546
$530$	−3.81417	−	2.77116i	−0.165677	−	0.120371i
$531$		0			0
$532$	0.969823	+	2.98481i	0.0420472	+	0.129408i
$533$	−21.3403	+	15.5046i	−0.924349	+	0.671579i
$534$		0			0
$535$	3.93919	+	12.1236i	0.170306	+	0.524148i
$536$	1.33239	−	4.10068i	0.0575506	−	0.177123i
$537$		0			0
$538$	7.70412			0.332148
$539$	−10.2671	+	10.2643i	−0.442236	+	0.442114i
$540$		0			0
$541$	14.3226	+	10.4060i	0.615777	+	0.447388i	0.851444	−	0.524446i	$-0.175728\pi$
$541$	14.3226	+	10.4060i	0.615777	+	0.447388i	−0.235667	+	0.971834i	$0.575728\pi$
$542$	3.93356	−	12.1063i	0.168961	−	0.520009i
$543$		0			0
$544$	12.5328	−	9.10562i	0.537340	−	0.390400i
$545$	−12.6169	+	9.16668i	−0.540447	+	0.392658i
$546$		0			0
$547$	1.78996	−	5.50893i	0.0765331	−	0.235545i	−0.905470	−	0.424411i	$-0.860481\pi$
$547$	1.78996	−	5.50893i	0.0765331	−	0.235545i	0.982003	+	0.188866i	$0.0604812\pi$
$548$	9.02219	+	6.55501i	0.385409	+	0.280016i
$549$		0			0
$550$	−1.13812	+	1.13780i	−0.0485294	+	0.0485160i
$551$	−3.89987			−0.166140
$552$		0			0
$553$	0.996831	−	3.06793i	0.0423896	−	0.130462i
$554$	0.976302	+	3.00475i	0.0414791	+	0.127660i
$555$		0			0
$556$	−20.1053	+	14.6074i	−0.852657	+	0.619491i
$557$	−12.7219	−	39.1539i	−0.539043	−	1.65901i	−0.734746	−	0.678342i	$-0.762699\pi$
$557$	−12.7219	−	39.1539i	−0.539043	−	1.65901i	0.195703	−	0.980663i	$-0.437301\pi$
$558$		0			0
$559$	−13.6811	−	9.93990i	−0.578649	−	0.420413i
$560$	−4.27988			−0.180858
$561$		0			0
$562$	−5.44367			−0.229627
$563$	−9.73841	−	7.07537i	−0.410425	−	0.298191i	0.363349	−	0.931653i	$-0.381633\pi$
$563$	−9.73841	−	7.07537i	−0.410425	−	0.298191i	−0.773774	+	0.633462i	$0.781633\pi$
$564$		0			0
$565$	−1.74092	−	5.35799i	−0.0732410	−	0.225412i
$566$	3.24901	−	2.36054i	0.136566	−	0.0992210i
$567$		0			0
$568$	9.40178	+	28.9357i	0.394490	+	1.21411i
$569$	1.14144	−	3.51299i	0.0478517	−	0.147272i	−0.924276	−	0.381725i	$-0.875330\pi$
$569$	1.14144	−	3.51299i	0.0478517	−	0.147272i	0.972127	+	0.234453i	$0.0753300\pi$
$570$		0			0
$571$	−5.17733			−0.216665			−0.108332	−	0.994115i	$-0.534551\pi$
$571$	−5.17733			−0.216665			−0.108332	+	0.994115i	$0.534551\pi$
$572$	4.54300	−	28.6578i	0.189952	−	1.19824i
$573$		0			0
$574$	−3.38234	−	2.45742i	−0.141176	−	0.102571i
$575$	2.08827	−	6.42703i	0.0870868	−	0.268026i
$576$		0			0
$577$	−0.796182	+	0.578460i	−0.0331455	+	0.0240816i	−0.604235	−	0.796806i	$-0.706521\pi$
$577$	−0.796182	+	0.578460i	−0.0331455	+	0.0240816i	0.571089	+	0.820888i	$0.306521\pi$
$578$	−2.80631	+	2.03890i	−0.116727	+	0.0848071i
$579$		0			0
$580$	1.93627	−	5.95924i	0.0803994	−	0.247444i
$581$	−12.5113	−	9.08999i	−0.519056	−	0.377116i
$582$		0			0
$583$	−28.7107	−	14.6338i	−1.18908	−	0.606071i
$584$	15.5184			0.642155
$585$		0			0
$586$	0.0627452	−	0.193110i	0.00259198	−	0.00797729i
$587$	9.78070	+	30.1019i	0.403693	+	1.24244i	0.921982	+	0.387233i	$0.126569\pi$
$587$	9.78070	+	30.1019i	0.403693	+	1.24244i	−0.518289	+	0.855205i	$0.673431\pi$
$588$		0			0
$589$	−7.58504	+	5.51085i	−0.312536	+	0.227071i
$590$	1.07741	+	3.31593i	0.0443563	+	0.136515i
$591$		0			0
$592$	11.4594	+	8.32573i	0.470978	+	0.342185i
$593$	−38.9330			−1.59879			−0.799394	−	0.600808i	$-0.794846\pi$
$593$	−38.9330			−1.59879			−0.799394	+	0.600808i	$0.794846\pi$
$594$		0			0
$595$	−5.08298			−0.208382
$596$	24.7645	+	17.9925i	1.01440	+	0.737001i
$597$		0			0
$598$	−5.02380	−	15.4617i	−0.205438	−	0.632274i
$599$	−1.37426	+	0.998461i	−0.0561509	+	0.0407960i	−0.615507	−	0.788132i	$-0.711049\pi$
$599$	−1.37426	+	0.998461i	−0.0561509	+	0.0407960i	0.559356	+	0.828928i	$0.311049\pi$
$600$		0			0
$601$	−12.6949	−	39.0710i	−0.517838	−	1.59374i	−0.778059	−	0.628192i	$-0.783795\pi$
$601$	−12.6949	−	39.0710i	−0.517838	−	1.59374i	0.260221	−	0.965549i	$-0.416205\pi$
$602$	0.828255	−	2.54911i	0.0337571	−	0.103894i
$603$		0			0
$604$	15.9067			0.647233
$605$	−6.46809	+	8.89740i	−0.262965	+	0.361731i
$606$		0			0
$607$	17.6712	+	12.8389i	0.717253	+	0.521115i	0.885505	−	0.464629i	$-0.153812\pi$
$607$	17.6712	+	12.8389i	0.717253	+	0.521115i	−0.168253	+	0.985744i	$0.553812\pi$
$608$	−1.67506	+	5.15529i	−0.0679325	+	0.209075i
$609$		0			0
$610$	−2.60460	+	1.89235i	−0.105457	+	0.0766192i
$611$	26.4792	−	19.2383i	1.07123	−	0.778297i
$612$		0			0
$613$	14.1471	−	43.5402i	0.571394	−	1.75857i	−0.0767464	−	0.997051i	$-0.524453\pi$
$613$	14.1471	−	43.5402i	0.571394	−	1.75857i	0.648141	−	0.761521i	$-0.275547\pi$
$614$	−12.8735	−	9.35317i	−0.519534	−	0.377463i
$615$		0			0
$616$	9.69077	−	1.53350i	0.390452	−	0.0617863i
$617$	37.0763			1.49263			0.746317	−	0.665590i	$-0.231820\pi$
$617$	37.0763			1.49263			0.746317	+	0.665590i	$0.231820\pi$
$618$		0			0
$619$	5.02300	−	15.4592i	0.201891	−	0.621358i	−0.797935	−	0.602743i	$-0.794074\pi$
$619$	5.02300	−	15.4592i	0.201891	−	0.621358i	0.999827	−	0.0186148i	$-0.00592562\pi$
$620$	−4.65497	−	14.3265i	−0.186948	−	0.575367i
$621$		0			0
$622$	−0.200048	+	0.145343i	−0.00802119	+	0.00582774i
$623$	−1.32804	−	4.08728i	−0.0532067	−	0.163753i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−1.37449			−0.0549358
$627$		0			0
$628$	−21.0624			−0.840482
$629$	13.6097	+	9.88801i	0.542653	+	0.394261i
$630$		0			0
$631$	−2.80690	−	8.63874i	−0.111741	−	0.343903i	0.879513	−	0.475876i	$-0.157869\pi$
$631$	−2.80690	−	8.63874i	−0.111741	−	0.343903i	−0.991253	+	0.131973i	$0.957869\pi$
$632$	2.94362	−	2.13866i	0.117091	−	0.0850715i
$633$		0			0
$634$	4.04717	+	12.4559i	0.160734	+	0.494687i
$635$	2.27526	−	7.00253i	0.0902909	−	0.277887i
$636$		0			0
$637$	−21.7024			−0.859880
$638$	−0.894749	+	5.64418i	−0.0354235	+	0.223455i
$639$		0			0
$640$	−9.12081	−	6.62665i	−0.360531	−	0.261941i
$641$	2.30363	−	7.08985i	0.0909879	−	0.280032i	−0.895199	−	0.445666i	$-0.852967\pi$
$641$	2.30363	−	7.08985i	0.0909879	−	0.280032i	0.986187	+	0.165634i	$0.0529670\pi$
$642$		0			0
$643$	−35.7255	+	25.9561i	−1.40888	+	1.02361i	−0.415391	+	0.909643i	$0.636355\pi$
$643$	−35.7255	+	25.9561i	−1.40888	+	1.02361i	−0.993485	+	0.113966i	$0.963645\pi$
$644$	−15.6232	+	11.3509i	−0.615641	+	0.447289i
$645$		0			0
$646$	−0.516861	+	1.59073i	−0.0203356	+	0.0625866i
$647$	−9.25415	−	6.72353i	−0.363818	−	0.264329i	0.390825	−	0.920465i	$-0.372190\pi$
$647$	−9.25415	−	6.72353i	−0.363818	−	0.264329i	−0.754643	+	0.656136i	$0.772190\pi$
$648$		0			0
$649$	10.8163	+	21.2355i	0.424578	+	0.833565i
$650$	−2.40572			−0.0943602
$651$		0			0
$652$	1.26909	−	3.90587i	0.0497016	−	0.152966i
$653$	−0.611505	−	1.88202i	−0.0239301	−	0.0736491i	0.938378	−	0.345610i	$-0.112328\pi$
$653$	−0.611505	−	1.88202i	−0.0239301	−	0.0736491i	−0.962308	+	0.271961i	$0.912328\pi$
$654$		0			0
$655$	5.45297	−	3.96181i	0.213065	−	0.154801i
$656$	4.34492	+	13.3723i	0.169641	+	0.522100i
$657$		0			0
$658$	4.19685	+	3.04919i	0.163610	+	0.118870i
$659$	18.3062			0.713107			0.356553	−	0.934275i	$-0.383952\pi$
$659$	18.3062			0.713107			0.356553	+	0.934275i	$0.383952\pi$
$660$		0			0
$661$	−1.16189			−0.0451922			−0.0225961	−	0.999745i	$-0.507193\pi$
$661$	−1.16189			−0.0451922			−0.0225961	+	0.999745i	$0.507193\pi$
$662$	8.45857	+	6.14551i	0.328752	+	0.238852i
$663$		0			0
$664$	−5.39029	−	16.5896i	−0.209184	−	0.643801i
$665$	1.43891	−	1.04543i	0.0557984	−	0.0405399i
$666$		0			0
$667$	−7.41542	−	22.8223i	−0.287126	−	0.883683i
$668$	−5.35704	+	16.4873i	−0.207270	+	0.637911i
$669$		0			0
$670$	−1.14535			−0.0442485
$671$	−15.5625	+	15.5582i	−0.600785	+	0.600619i
$672$		0			0
$673$	−1.06279	−	0.772159i	−0.0409674	−	0.0297645i	0.567113	−	0.823640i	$-0.308060\pi$
$673$	−1.06279	−	0.772159i	−0.0409674	−	0.0297645i	−0.608081	+	0.793875i	$0.708060\pi$
$674$	−1.64586	+	5.06545i	−0.0633963	+	0.195114i
$675$		0			0
$676$	16.5326	−	12.0117i	0.635871	−	0.461987i
$677$	15.5872	−	11.3248i	0.599064	−	0.435246i	−0.246482	−	0.969147i	$-0.579275\pi$
$677$	15.5872	−	11.3248i	0.599064	−	0.435246i	0.845547	+	0.533902i	$0.179275\pi$
$678$		0			0
$679$	7.26840	−	22.3698i	0.278936	−	0.858475i
$680$	−4.63832	−	3.36994i	−0.177872	−	0.129231i
$681$		0			0
$682$	6.23547	+	12.2420i	0.238769	+	0.468770i
$683$	−7.15293			−0.273699			−0.136850	−	0.990592i	$-0.543698\pi$
$683$	−7.15293			−0.273699			−0.136850	+	0.990592i	$0.543698\pi$
$684$		0			0
$685$	1.95300	−	6.01071i	0.0746202	−	0.229657i
$686$	−2.76274	−	8.50285i	−0.105482	−	0.324640i
$687$		0			0
$688$	−7.29254	+	5.29834i	−0.278025	+	0.201997i
$689$	−14.8861	−	45.8146i	−0.567114	−	1.74540i
$690$		0			0
$691$	−16.8534	−	12.2447i	−0.641134	−	0.465811i	0.219106	−	0.975701i	$-0.429686\pi$
$691$	−16.8534	−	12.2447i	−0.641134	−	0.465811i	−0.860240	+	0.509890i	$0.829686\pi$
$692$	−41.0083			−1.55890
$693$		0			0
$694$	−8.11259			−0.307950
$695$	11.3940	+	8.27823i	0.432199	+	0.314011i
$696$		0			0
$697$	5.16022	+	15.8815i	0.195457	+	0.601556i
$698$	1.80512	−	1.31150i	0.0683248	−	0.0496409i
$699$		0			0
$700$	0.883062	+	2.71779i	0.0333766	+	0.102723i
$701$	5.78777	−	17.8129i	0.218601	−	0.672785i	−0.780277	−	0.625434i	$-0.784922\pi$
$701$	5.78777	−	17.8129i	0.218601	−	0.672785i	0.998878	−	0.0473511i	$-0.0150780\pi$
$702$		0			0
$703$	−5.88636			−0.222008
$704$	−8.54153	−	4.35361i	−0.321921	−	0.164083i
$705$		0			0
$706$	−5.67745	−	4.12491i	−0.213674	−	0.155243i
$707$	−8.85424	+	27.2505i	−0.332998	+	1.02486i
$708$		0			0
$709$	14.5888	−	10.5994i	0.547895	−	0.398069i	−0.279114	−	0.960258i	$-0.590041\pi$
$709$	14.5888	−	10.5994i	0.547895	−	0.398069i	0.827009	+	0.562189i	$0.190041\pi$
$710$	6.53840	−	4.75043i	0.245382	−	0.178280i
$711$		0			0
$712$	1.49794	−	4.61019i	0.0561378	−	0.172774i
$713$	−46.6724	−	33.9095i	−1.74790	−	1.26992i
$714$		0			0
$715$	−16.2415	+	2.57011i	−0.607398	+	0.0961165i
$716$	0.664444			0.0248314
$717$		0			0
$718$	1.28447	−	3.95318i	0.0479359	−	0.147531i
$719$	12.1961	+	37.5357i	0.454837	+	1.39984i	0.871326	+	0.490704i	$0.163260\pi$
$719$	12.1961	+	37.5357i	0.454837	+	1.39984i	−0.416489	+	0.909141i	$0.636740\pi$
$720$		0			0
$721$	−6.46746	+	4.69889i	−0.240861	+	0.174996i
$722$	2.66807	+	8.21148i	0.0992953	+	0.305599i
$723$		0			0
$724$	−10.8231	−	7.86345i	−0.402238	−	0.292243i
$725$	−3.55099			−0.131880
$726$		0			0
$727$	12.4002			0.459899			0.229950	−	0.973203i	$-0.426144\pi$
$727$	12.4002			0.459899			0.229950	+	0.973203i	$0.426144\pi$
$728$	11.8656	+	8.62088i	0.439769	+	0.319511i
$729$		0			0
$730$	−1.27384	−	3.92048i	−0.0471470	−	0.145103i
$731$	−8.66095	+	6.29255i	−0.320337	+	0.232738i
$732$		0			0
$733$	3.38267	+	10.4108i	0.124942	+	0.384531i	0.993890	−	0.110371i	$-0.0352040\pi$
$733$	3.38267	+	10.4108i	0.124942	+	0.384531i	−0.868949	+	0.494902i	$0.835204\pi$
$734$	−0.172325	+	0.530362i	−0.00636063	+	0.0195760i
$735$		0			0
$736$	−33.3541			−1.22945
$737$	−7.73245	+	1.22361i	−0.284828	+	0.0450721i
$738$		0			0
$739$	−11.8963	−	8.64319i	−0.437614	−	0.317945i	0.347072	−	0.937838i	$-0.387176\pi$
$739$	−11.8963	−	8.64319i	−0.437614	−	0.317945i	−0.784686	+	0.619893i	$0.787176\pi$
$740$	2.92256	−	8.99470i	0.107435	−	0.330652i
$741$		0			0
$742$	6.17695	−	4.48781i	0.226763	−	0.164753i
$743$	23.3464	−	16.9622i	0.856498	−	0.622282i	−0.0704319	−	0.997517i	$-0.522438\pi$
$743$	23.3464	−	16.9622i	0.856498	−	0.622282i	0.926930	+	0.375234i	$0.122438\pi$
$744$		0			0
$745$	5.36068	−	16.4985i	0.196400	−	0.604458i
$746$	12.6148	+	9.16515i	0.461859	+	0.335560i
$747$		0			0
$748$	−16.3654	−	8.34143i	−0.598378	−	0.304993i
$749$	−20.6442			−0.754323
$750$		0			0
$751$	−7.95563	+	24.4849i	−0.290305	+	0.893467i	0.694453	+	0.719538i	$0.255646\pi$
$751$	−7.95563	+	24.4849i	−0.290305	+	0.893467i	−0.984758	+	0.173929i	$0.944354\pi$
$752$	−5.39122	−	16.5925i	−0.196598	−	0.605066i
$753$		0			0
$754$	−6.91119	+	5.02127i	−0.251691	+	0.182864i
$755$	−2.78565	−	8.57334i	−0.101380	−	0.312016i
$756$		0			0
$757$	−32.0812	−	23.3083i	−1.16601	−	0.847156i	−0.175485	−	0.984482i	$-0.556149\pi$
$757$	−32.0812	−	23.3083i	−1.16601	−	0.847156i	−0.990526	+	0.137326i	$0.956149\pi$
$758$	−7.15159			−0.259757
$759$		0			0
$760$	2.00613			0.0727701
$761$	25.2185	+	18.3223i	0.914170	+	0.664183i	0.942066	−	0.335427i	$-0.108881\pi$
$761$	25.2185	+	18.3223i	0.914170	+	0.664183i	−0.0278959	+	0.999611i	$0.508881\pi$
$762$		0			0
$763$	−7.80458	−	24.0200i	−0.282545	−	0.869583i
$764$	3.08925	−	2.24447i	0.111765	−	0.0812021i
$765$		0			0
$766$	−4.51161	−	13.8853i	−0.163011	−	0.501696i
$767$	−11.0087	+	33.8814i	−0.397502	+	1.22339i
$768$		0			0
$769$	−38.5273			−1.38933			−0.694666	−	0.719333i	$-0.744448\pi$
$769$	−38.5273			−1.38933			−0.694666	+	0.719333i	$0.744448\pi$
$770$	−1.18289	−	2.32234i	−0.0426284	−	0.0836915i
$771$		0			0
$772$	−26.5355	−	19.2792i	−0.955033	−	0.693872i
$773$	−13.2417	+	40.7537i	−0.476270	+	1.46581i	0.367967	+	0.929839i	$0.380054\pi$
$773$	−13.2417	+	40.7537i	−0.476270	+	1.46581i	−0.844237	+	0.535970i	$0.819946\pi$
$774$		0			0
$775$	−6.90648	+	5.01785i	−0.248088	+	0.180246i
$776$	21.4634	−	15.5941i	0.770492	−	0.559795i
$777$		0			0
$778$	5.19939	−	16.0021i	0.186407	−	0.573702i
$779$	−4.72716	−	3.43448i	−0.169368	−	0.123053i
$780$		0			0
$781$	39.0670	−	39.0562i	1.39793	−	1.39754i
$782$	−10.2919			−0.368036
$783$		0			0
$784$	−3.57477	+	11.0020i	−0.127670	+	0.392928i
$785$	3.68855	+	11.3522i	0.131650	+	0.405177i
$786$		0			0
$787$	−21.8827	+	15.8987i	−0.780035	+	0.566728i	−0.904989	−	0.425434i	$-0.860121\pi$
$787$	−21.8827	+	15.8987i	−0.780035	+	0.566728i	0.124955	+	0.992162i	$0.460121\pi$
$788$	4.74740	+	14.6110i	0.169119	+	0.520496i
$789$		0			0
$790$	−0.781930	−	0.568106i	−0.0278198	−	0.0202123i
$791$	9.12367			0.324400
$792$		0			0
$793$	−32.8957			−1.16816
$794$	14.3025	+	10.3914i	0.507576	+	0.368775i
$795$		0			0
$796$	10.3183	+	31.7566i	0.365724	+	1.12558i
$797$	−8.41045	+	6.11055i	−0.297913	+	0.216447i	−0.726693	−	0.686962i	$-0.758944\pi$
$797$	−8.41045	+	6.11055i	−0.297913	+	0.216447i	0.428780	+	0.903409i	$0.358944\pi$
$798$		0			0
$799$	−6.40286	−	19.7060i	−0.226517	−	0.697147i
$800$	−1.52521	+	4.69410i	−0.0539241	+	0.165961i
$801$		0			0
$802$	10.4535			0.369126
$803$	−12.7883	−	25.1070i	−0.451290	−	0.886008i
$804$		0			0
$805$	8.85391	+	6.43275i	0.312059	+	0.226724i
$806$	−6.34639	+	19.5322i	−0.223542	+	0.687992i
$807$		0			0
$808$	−26.1464	+	18.9964i	−0.919826	+	0.668293i
$809$	32.3120	−	23.4761i	1.13603	−	0.825375i	0.149470	−	0.988766i	$-0.452243\pi$
$809$	32.3120	−	23.4761i	1.13603	−	0.825375i	0.986561	+	0.163391i	$0.0522434\pi$
$810$		0			0
$811$	−4.81738	+	14.8264i	−0.169161	+	0.520625i	−0.999319	−	0.0369040i	$-0.988250\pi$
$811$	−4.81738	+	14.8264i	−0.169161	+	0.520625i	0.830158	+	0.557529i	$0.188250\pi$
$812$	8.20948	+	5.96454i	0.288096	+	0.209314i
$813$		0			0
$814$	−1.35051	+	8.51917i	−0.0473353	+	0.298597i
$815$	−2.32743			−0.0815263
$816$		0			0
$817$	1.15757	−	3.56263i	0.0404982	−	0.124641i
$818$	0.865844	+	2.66479i	0.0302735	+	0.0931723i
$819$		0			0
$820$	7.59511	−	5.51817i	0.265233	−	0.192703i
$821$	0.761411	+	2.34338i	0.0265734	+	0.0817846i	0.963464	−	0.267839i	$-0.0863095\pi$
$821$	0.761411	+	2.34338i	0.0265734	+	0.0817846i	−0.936890	+	0.349624i	$0.886310\pi$
$822$		0			0
$823$	44.6341	+	32.4286i	1.55585	+	1.13039i	0.939313	+	0.343060i	$0.111464\pi$
$823$	44.6341	+	32.4286i	1.55585	+	1.13039i	0.616534	+	0.787329i	$0.288536\pi$
$824$	−9.01698			−0.314122
$825$		0			0
$826$	−5.64642			−0.196464
$827$	−24.9101	−	18.0982i	−0.866208	−	0.629337i	0.0633584	−	0.997991i	$-0.479819\pi$
$827$	−24.9101	−	18.0982i	−0.866208	−	0.629337i	−0.929567	+	0.368654i	$0.879819\pi$
$828$		0			0
$829$	−7.99352	−	24.6015i	−0.277627	−	0.854447i	−0.988512	−	0.151139i	$-0.951706\pi$
$829$	−7.99352	−	24.6015i	−0.277627	−	0.854447i	0.710886	−	0.703307i	$-0.248294\pi$
$830$	−3.74864	+	2.72355i	−0.130117	+	0.0945357i
$831$		0			0
$832$	−4.42865	−	13.6300i	−0.153536	−	0.472535i
$833$	−4.24555	+	13.0665i	−0.147100	+	0.452726i
$834$		0			0
$835$	9.82442			0.339988
$836$	6.34837	−	1.00458i	0.219563	−	0.0347443i
$837$		0			0
$838$	5.28952	+	3.84306i	0.182723	+	0.132756i
$839$	16.2039	−	49.8704i	0.559420	−	1.72172i	−0.124555	−	0.992213i	$-0.539750\pi$
$839$	16.2039	−	49.8704i	0.559420	−	1.72172i	0.683975	−	0.729505i	$-0.260250\pi$
$840$		0			0
$841$	13.2602	−	9.63408i	0.457247	−	0.332210i
$842$	−9.51424	+	6.91250i	−0.327882	+	0.238221i
$843$		0			0
$844$	−9.46176	+	29.1203i	−0.325687	+	1.00236i
$845$	−9.36930	−	6.80720i	−0.322314	−	0.234175i
$846$		0			0
$847$	−10.4669	−	14.4149i	−0.359649	−	0.495301i
$848$	−25.6777			−0.881775
$849$		0			0
$850$	−0.470622	+	1.44843i	−0.0161422	+	0.0496806i
$851$	−11.1926	−	34.4473i	−0.383678	−	1.18084i
$852$		0			0
$853$	24.1701	−	17.5606i	0.827568	−	0.601263i	−0.0913024	−	0.995823i	$-0.529103\pi$
$853$	24.1701	−	17.5606i	0.827568	−	0.601263i	0.918870	+	0.394560i	$0.129103\pi$
$854$	−1.61116	−	4.95866i	−0.0551329	−	0.169682i
$855$		0			0
$856$	−18.8383	−	13.6868i	−0.643878	−	0.467805i
$857$	50.9131			1.73916			0.869579	−	0.493794i	$-0.164390\pi$
$857$	50.9131			1.73916			0.869579	+	0.493794i	$0.164390\pi$
$858$		0			0
$859$	30.2338			1.03156			0.515782	−	0.856720i	$-0.327501\pi$
$859$	30.2338			1.03156			0.515782	+	0.856720i	$0.327501\pi$
$860$	4.86918	+	3.53767i	0.166038	+	0.120633i
$861$		0			0
$862$	−0.116342	−	0.358063i	−0.00396261	−	0.0121957i
$863$	15.2158	−	11.0549i	0.517953	−	0.376315i	−0.297879	−	0.954604i	$-0.596279\pi$
$863$	15.2158	−	11.0549i	0.517953	−	0.376315i	0.815832	+	0.578289i	$0.196279\pi$
$864$		0			0
$865$	7.18156	+	22.1026i	0.244180	+	0.751509i
$866$	−5.18561	+	15.9597i	−0.176214	+	0.542331i
$867$		0			0
$868$	24.3954			0.828034
$869$	−5.88589	−	3.00003i	−0.199665	−	0.101769i
$870$		0			0
$871$	−9.46781	−	6.87877i	−0.320805	−	0.233078i
$872$	8.80308	−	27.0931i	0.298110	−	0.917488i
$873$		0			0
$874$	2.91345	−	2.11675i	0.0985490	−	0.0716000i
$875$	1.31018	−	0.951902i	0.0442922	−	0.0321802i
$876$		0			0
$877$	−13.9958	+	43.0748i	−0.472606	+	1.45453i	0.376553	+	0.926395i	$0.377109\pi$
$877$	−13.9958	+	43.0748i	−0.472606	+	1.45453i	−0.849159	+	0.528137i	$0.822891\pi$
$878$	2.84250	+	2.06520i	0.0959299	+	0.0696971i
$879$		0			0
$880$	−1.37235	+	8.65695i	−0.0462619	+	0.291826i
$881$	−24.6233			−0.829581			−0.414791	−	0.909917i	$-0.636145\pi$
$881$	−24.6233			−0.829581			−0.414791	+	0.909917i	$0.636145\pi$
$882$		0			0
$883$	17.2935	−	53.2239i	0.581972	−	1.79113i	−0.0291306	−	0.999576i	$-0.509274\pi$
$883$	17.2935	−	53.2239i	0.581972	−	1.79113i	0.611103	−	0.791551i	$-0.290726\pi$
$884$	−8.48522	−	26.1148i	−0.285389	−	0.878336i
$885$		0			0
$886$	2.12458	−	1.54360i	0.0713766	−	0.0518581i
$887$	7.27277	+	22.3833i	0.244196	+	0.751557i	0.995768	+	0.0919061i	$0.0292960\pi$
$887$	7.27277	+	22.3833i	0.244196	+	0.751557i	−0.751572	+	0.659651i	$0.770704\pi$
$888$		0			0
$889$	9.64672	+	7.00876i	0.323541	+	0.235066i
$890$	−1.28765			−0.0431623
$891$		0			0
$892$	−12.6886			−0.424846
$893$	5.86551	+	4.26154i	0.196282	+	0.142607i
$894$		0			0
$895$	−0.116360	−	0.358121i	−0.00388950	−	0.0119707i
$896$	14.7709	−	10.7317i	0.493461	−	0.358520i
$897$		0			0
$898$	1.93291	+	5.94887i	0.0645019	+	0.198516i
$899$	−9.36765	+	28.8307i	−0.312429	+	0.961557i
$900$		0			0
$901$	−30.4959			−1.01597
$902$	−6.05519	+	6.05352i	−0.201616	+	0.201560i
$903$		0			0
$904$	8.32554	+	6.04886i	0.276903	+	0.201182i
$905$	−2.34284	+	7.21051i	−0.0778785	+	0.239685i
$906$		0			0
$907$	36.9091	−	26.8161i	1.22555	−	0.890413i	0.229000	−	0.973427i	$-0.426455\pi$
$907$	36.9091	−	26.8161i	1.22555	−	0.890413i	0.996548	+	0.0830138i	$0.0264545\pi$
$908$	38.9740	−	28.3163i	1.29340	−	0.939708i
$909$		0			0
$910$	1.20393	−	3.70532i	0.0399099	−	0.122830i
$911$	−37.9352	−	27.5615i	−1.25685	−	0.913154i	−0.258251	−	0.966078i	$-0.583146\pi$
$911$	−37.9352	−	27.5615i	−1.25685	−	0.913154i	−0.998599	+	0.0529235i	$0.983146\pi$
$912$		0			0
$913$	−22.3982	+	22.3920i	−0.741271	+	0.741066i
$914$	−0.827531			−0.0273723
$915$		0			0
$916$	−6.74851	+	20.7698i	−0.222977	+	0.686253i
$917$	3.37312	+	10.3814i	0.111390	+	0.342824i
$918$		0			0
$919$	27.3480	−	19.8695i	0.902127	−	0.655434i	−0.0368841	−	0.999320i	$-0.511743\pi$
$919$	27.3480	−	19.8695i	0.902127	−	0.655434i	0.939012	+	0.343886i	$0.111743\pi$
$920$	3.81456	+	11.7400i	0.125762	+	0.387057i
$921$		0			0
$922$	11.7463	+	8.53421i	0.386845	+	0.281059i
$923$	82.5790			2.71812
$924$		0			0
$925$	−5.35976			−0.176228
$926$	−13.3377	−	9.69042i	−0.438304	−	0.318447i
$927$		0			0
$928$	5.41599	+	16.6687i	0.177789	+	0.547177i
$929$	12.5504	−	9.11842i	0.411766	−	0.299166i	−0.362550	−	0.931964i	$-0.618094\pi$
$929$	12.5504	−	9.11842i	0.411766	−	0.299166i	0.774316	+	0.632799i	$0.218094\pi$
$930$		0			0
$931$	−1.48556	−	4.57209i	−0.0486873	−	0.149844i
$932$	−7.93091	+	24.4088i	−0.259786	+	0.799538i
$933$		0			0
$934$	−0.0824506			−0.00269787
$935$	−1.62987	+	10.2814i	−0.0533023	+	0.336237i
$936$		0			0
$937$	3.51718	+	2.55538i	0.114901	+	0.0834806i	0.643752	−	0.765234i	$-0.277377\pi$
$937$	3.51718	+	2.55538i	0.114901	+	0.0834806i	−0.528851	+	0.848715i	$0.677377\pi$
$938$	0.573182	−	1.76407i	0.0187151	−	0.0575990i
$939$		0			0
$940$	−9.42409	+	6.84701i	−0.307380	+	0.223325i
$941$	−15.1392	+	10.9993i	−0.493525	+	0.358567i	−0.806538	−	0.591182i	$-0.798662\pi$
$941$	−15.1392	+	10.9993i	−0.493525	+	0.358567i	0.313013	+	0.949749i	$0.398662\pi$
$942$		0			0
$943$	11.1103	−	34.1941i	0.361803	−	1.11351i
$944$	15.3628	+	11.1617i	0.500016	+	0.363283i
$945$		0			0
$946$	−4.89052	−	2.49269i	−0.159004	−	0.0810444i
$947$	−18.6269			−0.605294			−0.302647	−	0.953103i	$-0.597870\pi$
$947$	−18.6269			−0.605294			−0.302647	+	0.953103i	$0.597870\pi$
$948$		0			0
$949$	13.0158	−	40.0585i	0.422511	−	1.30035i
$950$	−0.164675	−	0.506819i	−0.00534277	−	0.0164434i
$951$		0			0
$952$	7.51164	−	5.45753i	0.243454	−	0.176879i
$953$	−2.70176	−	8.31516i	−0.0875185	−	0.269354i	0.897713	−	0.440580i	$-0.145227\pi$
$953$	−2.70176	−	8.31516i	−0.0875185	−	0.269354i	−0.985232	+	0.171226i	$0.945227\pi$
$954$		0			0
$955$	−1.75072	−	1.27198i	−0.0566521	−	0.0411602i
$956$	−51.0428			−1.65084
$957$		0			0
$958$	−7.09304			−0.229166
$959$	8.28039	+	6.01605i	0.267388	+	0.194269i
$960$		0			0
$961$	12.9411	+	39.8286i	0.417455	+	1.28479i
$962$	−10.4315	+	7.57896i	−0.336326	+	0.244355i
$963$		0			0
$964$	5.12893	+	15.7852i	0.165192	+	0.508408i
$965$	−5.74403	+	17.6783i	−0.184907	+	0.569085i
$966$		0			0
$967$	47.6843			1.53342			0.766712	−	0.641992i	$-0.221892\pi$
$967$	47.6843			1.53342			0.766712	+	0.641992i	$0.221892\pi$
$968$	0.00554448	−	20.0933i	0.000178206	−	0.645823i
$969$		0			0
$970$	−5.70145	−	4.14235i	−0.183063	−	0.133003i
$971$	−10.1428	+	31.2165i	−0.325499	+	1.00178i	0.645715	+	0.763578i	$0.276559\pi$
$971$	−10.1428	+	31.2165i	−0.325499	+	1.00178i	−0.971215	+	0.238206i	$0.923441\pi$
$972$		0			0
$973$	−18.4523	+	13.4064i	−0.591553	+	0.429789i
$974$	−9.40252	+	6.83133i	−0.301276	+	0.218890i
$975$		0			0
$976$	−5.41850	+	16.6764i	−0.173442	+	0.533800i
$977$	−37.3174	−	27.1127i	−1.19389	−	0.867412i	−0.200220	−	0.979751i	$-0.564166\pi$
$977$	−37.3174	−	27.1127i	−1.19389	−	0.867412i	−0.993670	+	0.112339i	$0.964166\pi$
$978$		0			0
$979$	−8.69320	+	1.37564i	−0.277836	+	0.0439656i
$980$	7.72400			0.246734
$981$		0			0
$982$	−4.75752	+	14.6422i	−0.151819	+	0.467250i
$983$	4.99698	+	15.3791i	0.159379	+	0.490518i	0.998578	−	0.0533060i	$-0.0169759\pi$
$983$	4.99698	+	15.3791i	0.159379	+	0.490518i	−0.839199	+	0.543824i	$0.816976\pi$
$984$		0			0
$985$	7.04363	−	5.11750i	0.224429	−	0.163057i
$986$	1.67117	+	5.14334i	0.0532210	+	0.163797i
$987$		0			0
$988$	7.77311	+	5.64749i	0.247295	+	0.179671i
$989$	23.0498			0.732940
$990$		0			0
$991$	60.7308			1.92918			0.964589	−	0.263758i	$-0.0849622\pi$
$991$	60.7308			1.92918			0.964589	+	0.263758i	$0.0849622\pi$
$992$	34.0881	+	24.7664i	1.08230	+	0.786335i
$993$		0			0
$994$	4.04455	+	12.4478i	0.128285	+	0.394822i
$995$	15.3091	−	11.1227i	0.485332	−	0.352614i
$996$		0			0
$997$	−14.5212	−	44.6916i	−0.459890	−	1.41540i	−0.865297	−	0.501260i	$-0.832870\pi$
$997$	−14.5212	−	44.6916i	−0.459890	−	1.41540i	0.405407	−	0.914137i	$-0.367130\pi$
$998$	−4.96338	+	15.2757i	−0.157113	+	0.483544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.g.136.3	yes	16
3.2	odd	2		495.2.n.h.136.2	yes	16
11.3	even	5	inner	495.2.n.g.91.3	✓	16
11.5	even	5		5445.2.a.cd.1.3		8
11.6	odd	10		5445.2.a.cb.1.6		8
33.5	odd	10		5445.2.a.ca.1.6		8
33.14	odd	10		495.2.n.h.91.2	yes	16
33.17	even	10		5445.2.a.cc.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.91.3	✓	16	11.3	even	5	inner
495.2.n.g.136.3	yes	16	1.1	even	1	trivial
495.2.n.h.91.2	yes	16	33.14	odd	10
495.2.n.h.136.2	yes	16	3.2	odd	2
5445.2.a.ca.1.6		8	33.5	odd	10
5445.2.a.cb.1.6		8	11.6	odd	10
5445.2.a.cc.1.3		8	33.17	even	10
5445.2.a.cd.1.3		8	11.5	even	5

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.392557 + 0.285209i) q^{2} +(-0.545277 - 1.67819i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.500445 - 1.54021i) q^{7} +(0.564470 - 1.73726i) q^{8} +O(q^{10})\)	\(q+(0.392557 + 0.285209i) q^{2} +(-0.545277 - 1.67819i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-0.500445 - 1.54021i) q^{7} +(0.564470 - 1.73726i) q^{8} -0.485227 q^{10} +(-3.27586 + 0.518382i) q^{11} +(-4.01105 - 2.91420i) q^{13} +(0.242829 - 0.747352i) q^{14} +(-2.13804 + 1.55338i) q^{16} +(-2.53923 + 1.84486i) q^{17} +(0.339378 - 1.04450i) q^{19} +(1.42755 + 1.03718i) q^{20} +(-1.43381 - 0.730812i) q^{22} +6.75778 q^{23} +(0.309017 - 0.951057i) q^{25} +(-0.743409 - 2.28798i) q^{26} +(-2.31189 + 1.67968i) q^{28} +(-1.09732 - 3.37719i) q^{29} +(-6.90648 - 5.01785i) q^{31} -4.93567 q^{32} -1.52296 q^{34} +(1.31018 + 0.951902i) q^{35} +(-1.65626 - 5.09743i) q^{37} +(0.431126 - 0.313231i) q^{38} +(0.564470 + 1.73726i) q^{40} +(1.64408 - 5.05997i) q^{41} +3.41085 q^{43} +(2.65620 + 5.21486i) q^{44} +(2.65281 + 1.92738i) q^{46} +(-2.04000 + 6.27846i) q^{47} +(3.54132 - 2.57292i) q^{49} +(0.392557 - 0.285209i) q^{50} +(-2.70345 + 8.32036i) q^{52} +(7.86059 + 5.71105i) q^{53} +(2.34553 - 2.34488i) q^{55} -2.95823 q^{56} +(0.532447 - 1.63870i) q^{58} +(-2.22043 - 6.83377i) q^{59} +(5.36780 - 3.89994i) q^{61} +(-1.28005 - 3.93958i) q^{62} +(2.33855 + 1.69906i) q^{64} +4.95793 q^{65} +2.36043 q^{67} +(4.48061 + 3.25536i) q^{68} +(0.242829 + 0.747352i) q^{70} +(-13.4749 + 9.79011i) q^{71} +(2.62525 + 8.07968i) q^{73} +(0.803661 - 2.47341i) q^{74} -1.93792 q^{76} +(2.43781 + 4.78610i) q^{77} +(1.61147 + 1.17080i) q^{79} +(0.816659 - 2.51342i) q^{80} +(2.08855 - 1.51742i) q^{82} +(7.72554 - 5.61293i) q^{83} +(0.969900 - 2.98505i) q^{85} +(1.33895 + 0.972807i) q^{86} +(-0.948562 + 5.98364i) q^{88} +2.65371 q^{89} +(-2.48117 + 7.63626i) q^{91} +(-3.68486 - 11.3408i) q^{92} +(-2.59149 + 1.88283i) q^{94} +(0.339378 + 1.04450i) q^{95} +(11.7501 + 8.53692i) q^{97} +2.12399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8	\( 16 q - 2 q^{2} - 8 q^{4} - 4 q^{5} - 4 q^{7} - 6 q^{8} + 8 q^{10} + 4 q^{11} + 2 q^{13} - 22 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} + 2 q^{20} - 28 q^{22} + 8 q^{23} - 4 q^{25} + 6 q^{26} - 2 q^{28} - 26 q^{29} - 10 q^{31} + 56 q^{32} - 4 q^{34} - 4 q^{35} + 22 q^{37} - 30 q^{38} - 6 q^{40} - 6 q^{41} + 28 q^{43} + 68 q^{44} + 16 q^{46} - 20 q^{47} + 10 q^{49} - 2 q^{50} + 30 q^{52} + 14 q^{53} - 6 q^{55} + 68 q^{56} - 6 q^{58} - 16 q^{59} - 38 q^{61} - 20 q^{62} + 10 q^{64} + 12 q^{65} + 20 q^{67} - 48 q^{68} - 22 q^{70} - 54 q^{71} + 2 q^{73} + 28 q^{74} - 44 q^{76} + 34 q^{77} - 12 q^{79} - 22 q^{80} + 30 q^{82} - 28 q^{83} - 4 q^{85} + 74 q^{86} + 46 q^{88} + 76 q^{89} - 34 q^{91} - 8 q^{92} - 10 q^{94} - 4 q^{95} - 18 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 8 * q^4 - 4 * q^5 - 4 * q^7 - 6 * q^8 + 8 * q^10 + 4 * q^11 + 2 * q^13 - 22 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 + 2 * q^20 - 28 * q^22 + 8 * q^23 - 4 * q^25 + 6 * q^26 - 2 * q^28 - 26 * q^29 - 10 * q^31 + 56 * q^32 - 4 * q^34 - 4 * q^35 + 22 * q^37 - 30 * q^38 - 6 * q^40 - 6 * q^41 + 28 * q^43 + 68 * q^44 + 16 * q^46 - 20 * q^47 + 10 * q^49 - 2 * q^50 + 30 * q^52 + 14 * q^53 - 6 * q^55 + 68 * q^56 - 6 * q^58 - 16 * q^59 - 38 * q^61 - 20 * q^62 + 10 * q^64 + 12 * q^65 + 20 * q^67 - 48 * q^68 - 22 * q^70 - 54 * q^71 + 2 * q^73 + 28 * q^74 - 44 * q^76 + 34 * q^77 - 12 * q^79 - 22 * q^80 + 30 * q^82 - 28 * q^83 - 4 * q^85 + 74 * q^86 + 46 * q^88 + 76 * q^89 - 34 * q^91 - 8 * q^92 - 10 * q^94 - 4 * q^95 - 18 * q^97 + 8 * q^98

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