LMFDB - Embedded newform 297.2.f.a.82.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (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:	$2.37155694003$
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} + 8 x^{14} - 22 x^{13} + 62 x^{12} - 24 x^{11} + 152 x^{10} - 161 x^{9} + 552 x^{8} + \cdots + 25 $ x^16 - 2x^15 + 8x^14 - 22x^13 + 62x^12 - 24x^11 + 152x^10 - 161x^9 + 552x^8 - 609x^7 + 1150x^6 - 862x^5 + 1346x^4 - 235x^3 + 340x^2 + 150*x + 25
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			82.4
Root			$0.416955 - 1.28326i$ of defining polynomial
Character	$\chi$	$=$	297.82
Dual form			297.2.f.a.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.725972 + 2.23431i) q^{2} +(-2.84709 + 2.06853i) q^{4} +(-1.06108 + 3.26568i) q^{5} +(2.30657 - 1.67582i) q^{7} +(-2.88741 - 2.09782i) q^{8} +O(q^{10})$	\(q+(0.725972 + 2.23431i) q^{2} +(-2.84709 + 2.06853i) q^{4} +(-1.06108 + 3.26568i) q^{5} +(2.30657 - 1.67582i) q^{7} +(-2.88741 - 2.09782i) q^{8} -8.06687 q^{10} +(-3.10533 + 1.16487i) q^{11} +(0.236903 + 0.729111i) q^{13} +(5.41882 + 3.93700i) q^{14} +(0.416037 - 1.28043i) q^{16} +(1.17053 - 3.60253i) q^{17} +(-2.30182 - 1.67237i) q^{19} +(-3.73416 - 11.4926i) q^{20} +(-4.85707 - 6.09262i) q^{22} +8.97543 q^{23} +(-5.49369 - 3.99140i) q^{25} +(-1.45708 + 1.05863i) q^{26} +(-3.10052 + 9.54242i) q^{28} +(-1.90644 + 1.38511i) q^{29} +(2.86520 + 8.81819i) q^{31} -3.97515 q^{32} +8.89897 q^{34} +(3.02524 + 9.31072i) q^{35} +(3.67146 - 2.66747i) q^{37} +(2.06554 - 6.35708i) q^{38} +(9.91460 - 7.20338i) q^{40} +(-3.71324 - 2.69783i) q^{41} +10.2443 q^{43} +(6.43157 - 9.73995i) q^{44} +(6.51591 + 20.0539i) q^{46} +(3.08604 + 2.24214i) q^{47} +(0.348772 - 1.07341i) q^{49} +(4.92977 - 15.1723i) q^{50} +(-2.18267 - 1.58580i) q^{52} +(1.93120 + 5.94363i) q^{53} +(-0.509080 - 11.3770i) q^{55} -10.1756 q^{56} +(-4.47879 - 3.25403i) q^{58} +(-1.15621 + 0.840035i) q^{59} +(0.169928 - 0.522984i) q^{61} +(-17.6225 + 12.8035i) q^{62} +(-3.71792 - 11.4426i) q^{64} -2.63242 q^{65} -8.14064 q^{67} +(4.11933 + 12.6780i) q^{68} +(-18.6068 + 13.5186i) q^{70} +(3.14891 - 9.69134i) q^{71} +(13.2714 - 9.64225i) q^{73} +(8.62535 + 6.26669i) q^{74} +10.0128 q^{76} +(-5.21055 + 7.89084i) q^{77} +(0.890062 + 2.73933i) q^{79} +(3.74003 + 2.71729i) q^{80} +(3.33208 - 10.2551i) q^{82} +(0.500768 - 1.54120i) q^{83} +(10.5227 + 7.64519i) q^{85} +(7.43709 + 22.8890i) q^{86} +(11.4100 + 3.15098i) q^{88} -1.72157 q^{89} +(1.76829 + 1.28474i) q^{91} +(-25.5538 + 18.5659i) q^{92} +(-2.76926 + 8.52292i) q^{94} +(7.90385 - 5.74248i) q^{95} +(-3.19949 - 9.84701i) q^{97} +2.65153 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7	$ 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7} + 6 q^{10} - 13 q^{11} - 2 q^{13} + 22 q^{14} - 24 q^{16} + 2 q^{17} - 2 q^{19} + 15 q^{22} - 14 q^{23} - 19 q^{25} - 21 q^{26} + 15 q^{28} - q^{29} + 14 q^{31} + 48 q^{32} + 10 q^{34} + 18 q^{35} + 9 q^{37} - 11 q^{38} + 33 q^{40} - 25 q^{41} + 14 q^{43} - 14 q^{44} + 4 q^{46} + 28 q^{47} - 4 q^{49} + 63 q^{50} + 10 q^{52} - q^{53} - 40 q^{55} - 96 q^{56} - 20 q^{58} - 41 q^{59} + 5 q^{62} - 92 q^{64} + 60 q^{65} - 48 q^{67} - 25 q^{68} - 31 q^{70} - 3 q^{71} - 13 q^{73} - 29 q^{74} - 58 q^{76} + 2 q^{77} + 83 q^{80} + 41 q^{82} + 14 q^{83} - 10 q^{85} + 56 q^{86} + 86 q^{88} - 82 q^{89} + 14 q^{91} - 74 q^{92} - 2 q^{94} + 56 q^{95} + 12 q^{97} - 26 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7 + 6 * q^10 - 13 * q^11 - 2 * q^13 + 22 * q^14 - 24 * q^16 + 2 * q^17 - 2 * q^19 + 15 * q^22 - 14 * q^23 - 19 * q^25 - 21 * q^26 + 15 * q^28 - q^29 + 14 * q^31 + 48 * q^32 + 10 * q^34 + 18 * q^35 + 9 * q^37 - 11 * q^38 + 33 * q^40 - 25 * q^41 + 14 * q^43 - 14 * q^44 + 4 * q^46 + 28 * q^47 - 4 * q^49 + 63 * q^50 + 10 * q^52 - q^53 - 40 * q^55 - 96 * q^56 - 20 * q^58 - 41 * q^59 + 5 * q^62 - 92 * q^64 + 60 * q^65 - 48 * q^67 - 25 * q^68 - 31 * q^70 - 3 * q^71 - 13 * q^73 - 29 * q^74 - 58 * q^76 + 2 * q^77 + 83 * q^80 + 41 * q^82 + 14 * q^83 - 10 * q^85 + 56 * q^86 + 86 * q^88 - 82 * q^89 + 14 * q^91 - 74 * q^92 - 2 * q^94 + 56 * q^95 + 12 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.725972	+	2.23431i	0.513340	+	1.57990i	0.786282	+	0.617868i	$0.212003\pi$
$2$	0.725972	+	2.23431i	0.513340	+	1.57990i	−0.272942	+	0.962030i	$0.587997\pi$
$3$		0			0
$3$		0			0
$4$	−2.84709	+	2.06853i	−1.42354	+	1.03426i
$5$	−1.06108	+	3.26568i	−0.474531	+	1.46046i	0.372057	+	0.928210i	$0.378652\pi$
$5$	−1.06108	+	3.26568i	−0.474531	+	1.46046i	−0.846589	+	0.532248i	$0.821348\pi$
$6$		0			0
$7$	2.30657	−	1.67582i	0.871802	−	0.633401i	−0.0592680	−	0.998242i	$-0.518877\pi$
$7$	2.30657	−	1.67582i	0.871802	−	0.633401i	0.931070	+	0.364841i	$0.118877\pi$
$8$	−2.88741	−	2.09782i	−1.02085	−	0.741692i
$9$		0			0
$10$	−8.06687			−2.55097
$11$	−3.10533	+	1.16487i	−0.936292	+	0.351222i
$11$	−3.10533	+	1.16487i	−0.936292	+	0.351222i
$12$		0			0
$13$	0.236903	+	0.729111i	0.0657050	+	0.202219i	0.978519	−	0.206156i	$-0.0660955\pi$
$13$	0.236903	+	0.729111i	0.0657050	+	0.202219i	−0.912814	+	0.408375i	$0.866095\pi$
$14$	5.41882	+	3.93700i	1.44824	+	1.05221i
$15$		0			0
$16$	0.416037	−	1.28043i	0.104009	−	0.320107i
$17$	1.17053	−	3.60253i	0.283896	−	0.873743i	−0.702831	−	0.711357i	$-0.748081\pi$
$17$	1.17053	−	3.60253i	0.283896	−	0.873743i	0.986727	−	0.162386i	$-0.0519190\pi$
$18$		0			0
$19$	−2.30182	−	1.67237i	−0.528073	−	0.383668i	0.291563	−	0.956552i	$-0.405825\pi$
$19$	−2.30182	−	1.67237i	−0.528073	−	0.383668i	−0.819637	+	0.572884i	$0.805825\pi$
$20$	−3.73416	−	11.4926i	−0.834983	−	2.56981i
$21$		0			0
$22$	−4.85707	−	6.09262i	−1.03553	−	1.29895i
$23$	8.97543			1.87151			0.935753	−	0.352657i	$-0.114722\pi$
$23$	8.97543			1.87151			0.935753	+	0.352657i	$0.114722\pi$
$24$		0			0
$25$	−5.49369	−	3.99140i	−1.09874	−	0.798280i
$26$	−1.45708	+	1.05863i	−0.285757	+	0.207614i
$27$		0			0
$28$	−3.10052	+	9.54242i	−0.585943	+	1.80335i
$29$	−1.90644	+	1.38511i	−0.354017	+	0.257208i	−0.750552	−	0.660811i	$-0.770212\pi$
$29$	−1.90644	+	1.38511i	−0.354017	+	0.257208i	0.396535	+	0.918019i	$0.370212\pi$
$30$		0			0
$31$	2.86520	+	8.81819i	0.514606	+	1.58379i	0.783998	+	0.620763i	$0.213177\pi$
$31$	2.86520	+	8.81819i	0.514606	+	1.58379i	−0.269393	+	0.963030i	$0.586823\pi$
$32$	−3.97515			−0.702713
$33$		0			0
$34$	8.89897			1.52616
$35$	3.02524	+	9.31072i	0.511358	+	1.57380i
$36$		0			0
$37$	3.67146	−	2.66747i	0.603585	−	0.438530i	−0.243565	−	0.969885i	$-0.578317\pi$
$37$	3.67146	−	2.66747i	0.603585	−	0.438530i	0.847149	+	0.531355i	$0.178317\pi$
$38$	2.06554	−	6.35708i	0.335075	−	1.03125i
$39$		0			0
$40$	9.91460	−	7.20338i	1.56764	−	1.13895i
$41$	−3.71324	−	2.69783i	−0.579911	−	0.421330i	0.258781	−	0.965936i	$-0.416679\pi$
$41$	−3.71324	−	2.69783i	−0.579911	−	0.421330i	−0.838692	+	0.544606i	$0.816679\pi$
$42$		0			0
$43$	10.2443			1.56224			0.781121	−	0.624379i	$-0.214648\pi$
$43$	10.2443			1.56224			0.781121	+	0.624379i	$0.214648\pi$
$44$	6.43157	−	9.73995i	0.969596	−	1.46835i
$45$		0			0
$46$	6.51591	+	20.0539i	0.960719	+	2.95679i
$47$	3.08604	+	2.24214i	0.450146	+	0.327050i	0.789653	−	0.613553i	$-0.210260\pi$
$47$	3.08604	+	2.24214i	0.450146	+	0.327050i	−0.339508	+	0.940603i	$0.610260\pi$
$48$		0			0
$49$	0.348772	−	1.07341i	0.0498245	−	0.153344i
$50$	4.92977	−	15.1723i	0.697175	−	2.14568i
$51$		0			0
$52$	−2.18267	−	1.58580i	−0.302682	−	0.219911i
$53$	1.93120	+	5.94363i	0.265271	+	0.816420i	0.991631	+	0.129105i	$0.0412106\pi$
$53$	1.93120	+	5.94363i	0.265271	+	0.816420i	−0.726360	+	0.687315i	$0.758789\pi$
$54$		0			0
$55$	−0.509080	−	11.3770i	−0.0686444	−	1.53408i
$56$	−10.1756			−1.35977
$57$		0			0
$58$	−4.47879	−	3.25403i	−0.588094	−	0.427275i
$59$	−1.15621	+	0.840035i	−0.150526	+	0.109363i	−0.660499	−	0.750827i	$-0.729655\pi$
$59$	−1.15621	+	0.840035i	−0.150526	+	0.109363i	0.509973	+	0.860190i	$0.329655\pi$
$60$		0			0
$61$	0.169928	−	0.522984i	0.0217570	−	0.0669612i	−0.939589	−	0.342306i	$-0.888792\pi$
$61$	0.169928	−	0.522984i	0.0217570	−	0.0669612i	0.961346	+	0.275345i	$0.0887920\pi$
$62$	−17.6225	+	12.8035i	−2.23806	+	1.62605i
$63$		0			0
$64$	−3.71792	−	11.4426i	−0.464740	−	1.43032i
$65$	−2.63242			−0.326511
$66$		0			0
$67$	−8.14064			−0.994538			−0.497269	−	0.867597i	$-0.665664\pi$
$67$	−8.14064			−0.994538			−0.497269	+	0.867597i	$0.665664\pi$
$68$	4.11933	+	12.6780i	0.499543	+	1.53743i
$69$		0			0
$70$	−18.6068	+	13.5186i	−2.22394	+	1.61579i
$71$	3.14891	−	9.69134i	0.373707	−	1.15015i	−0.570641	−	0.821200i	$-0.693305\pi$
$71$	3.14891	−	9.69134i	0.373707	−	1.15015i	0.944347	−	0.328951i	$-0.106695\pi$
$72$		0			0
$73$	13.2714	−	9.64225i	1.55330	−	1.12854i	0.612057	−	0.790813i	$-0.290342\pi$
$73$	13.2714	−	9.64225i	1.55330	−	1.12854i	0.941244	−	0.337726i	$-0.109658\pi$
$74$	8.62535	+	6.26669i	1.00268	+	0.728487i
$75$		0			0
$76$	10.0128			1.14855
$77$	−5.21055	+	7.89084i	−0.593797	+	0.899244i
$78$		0			0
$79$	0.890062	+	2.73933i	0.100140	+	0.308199i	0.988559	−	0.150834i	$-0.0481960\pi$
$79$	0.890062	+	2.73933i	0.100140	+	0.308199i	−0.888419	+	0.459033i	$0.848196\pi$
$80$	3.74003	+	2.71729i	0.418148	+	0.303802i
$81$		0			0
$82$	3.33208	−	10.2551i	0.367967	−	1.13248i
$83$	0.500768	−	1.54120i	0.0549664	−	0.169169i	−0.919804	−	0.392377i	$-0.871653\pi$
$83$	0.500768	−	1.54120i	0.0549664	−	0.169169i	0.974771	+	0.223208i	$0.0716529\pi$
$84$		0			0
$85$	10.5227	+	7.64519i	1.14135	+	0.829237i
$86$	7.43709	+	22.8890i	0.801962	+	2.46818i
$87$		0			0
$88$	11.4100	+	3.15098i	1.21631	+	0.335895i
$89$	−1.72157			−0.182486			−0.0912430	−	0.995829i	$-0.529084\pi$
$89$	−1.72157			−0.182486			−0.0912430	+	0.995829i	$0.529084\pi$
$90$		0			0
$91$	1.76829	+	1.28474i	0.185368	+	0.134677i
$92$	−25.5538	+	18.5659i	−2.66417	+	1.93563i
$93$		0			0
$94$	−2.76926	+	8.52292i	−0.285628	+	0.879072i
$95$	7.90385	−	5.74248i	0.810918	−	0.589166i
$96$		0			0
$97$	−3.19949	−	9.84701i	−0.324859	−	0.999812i	−0.971504	−	0.237022i	$-0.923829\pi$
$97$	−3.19949	−	9.84701i	−0.324859	−	0.999812i	0.646646	−	0.762791i	$-0.276171\pi$
$98$	2.65153			0.267845
$99$		0			0
$100$	23.8973			2.38973
$101$	−1.91689	−	5.89958i	−0.190738	−	0.587030i	0.809262	−	0.587448i	$-0.199867\pi$
$101$	−1.91689	−	5.89958i	−0.190738	−	0.587030i	−1.00000		0.000417360i	$0.999867\pi$
$102$		0			0
$103$	−4.41834	+	3.21011i	−0.435352	+	0.316302i	−0.783785	−	0.621032i	$-0.786714\pi$
$103$	−4.41834	+	3.21011i	−0.435352	+	0.316302i	0.348433	+	0.937334i	$0.386714\pi$
$104$	0.845512	−	2.60222i	0.0829093	−	0.255169i
$105$		0			0
$106$	−11.8779	+	8.62982i	−1.15369	+	0.838202i
$107$	−7.22474	−	5.24908i	−0.698442	−	0.507448i	0.180983	−	0.983486i	$-0.442072\pi$
$107$	−7.22474	−	5.24908i	−0.698442	−	0.507448i	−0.879424	+	0.476039i	$0.842072\pi$
$108$		0			0
$109$	−2.42885			−0.232642			−0.116321	−	0.993212i	$-0.537110\pi$
$109$	−2.42885			−0.232642			−0.116321	+	0.993212i	$0.537110\pi$
$110$	25.0503	−	9.39687i	2.38845	−	0.895956i
$111$		0			0
$112$	−1.18615	−	3.65060i	−0.112081	−	0.344950i
$113$	−9.26885	−	6.73422i	−0.871941	−	0.633502i	0.0591664	−	0.998248i	$-0.481156\pi$
$113$	−9.26885	−	6.73422i	−0.871941	−	0.633502i	−0.931107	+	0.364746i	$0.881156\pi$
$114$		0			0
$115$	−9.52368	+	29.3109i	−0.888088	+	2.73325i
$116$	2.56266	−	7.88705i	0.237937	−	0.732294i
$117$		0			0
$118$	−2.71628	−	1.97349i	−0.250054	−	0.181675i
$119$	−3.33729	−	10.2711i	−0.305928	−	0.941551i
$120$		0			0
$121$	8.28615	−	7.23462i	0.753287	−	0.657692i
$122$	1.29187			0.116961
$123$		0			0
$124$	−26.3982	−	19.1794i	−2.37062	−	1.72236i
$125$	4.97415	−	3.61393i	0.444901	−	0.323240i
$126$		0			0
$127$	0.236065	−	0.726534i	0.0209474	−	0.0644695i	−0.940036	−	0.341074i	$-0.889209\pi$
$127$	0.236065	−	0.726534i	0.0209474	−	0.0644695i	0.960984	+	0.276605i	$0.0892093\pi$
$128$	16.4353	−	11.9409i	1.45269	−	1.05544i
$129$		0			0
$130$	−1.91106	−	5.88165i	−0.167611	−	0.515855i
$131$	−1.38902			−0.121359			−0.0606796	−	0.998157i	$-0.519327\pi$
$131$	−1.38902			−0.121359			−0.0606796	+	0.998157i	$0.519327\pi$
$132$		0			0
$133$	−8.11190			−0.703391
$134$	−5.90988	−	18.1887i	−0.510536	−	1.57127i
$135$		0			0
$136$	−10.9373	+	7.94640i	−0.937865	+	0.681398i
$137$	−1.65169	+	5.08338i	−0.141113	+	0.434302i	−0.996491	−	0.0837031i	$-0.973325\pi$
$137$	−1.65169	+	5.08338i	−0.141113	+	0.434302i	0.855377	+	0.518005i	$0.173325\pi$
$138$		0			0
$139$	4.25881	−	3.09421i	0.361227	−	0.262447i	−0.392336	−	0.919822i	$-0.628333\pi$
$139$	4.25881	−	3.09421i	0.361227	−	0.262447i	0.753564	+	0.657375i	$0.228333\pi$
$140$	−27.8726	−	20.2506i	−2.35566	−	1.71149i
$141$		0			0
$142$	23.9395			2.00896
$143$	−1.58498	−	1.98817i	−0.132543	−	0.166259i
$144$		0			0
$145$	−2.50043	−	7.69554i	−0.207650	−	0.639080i
$146$	31.1785	+	22.6525i	2.58035	+	1.87473i
$147$		0			0
$148$	−4.93522	+	15.1891i	−0.405673	+	1.24853i
$149$	4.63037	−	14.2508i	0.379335	−	1.16747i	−0.561172	−	0.827699i	$-0.689649\pi$
$149$	4.63037	−	14.2508i	0.379335	−	1.16747i	0.940507	−	0.339774i	$-0.110351\pi$
$150$		0			0
$151$	−2.19310	−	1.59338i	−0.178472	−	0.129668i	0.494962	−	0.868914i	$-0.335182\pi$
$151$	−2.19310	−	1.59338i	−0.178472	−	0.129668i	−0.673435	+	0.739247i	$0.735182\pi$
$152$	3.13795	+	9.65761i	0.254521	+	0.783336i
$153$		0			0
$154$	−21.4133	−	5.91347i	−1.72553	−	0.476521i
$155$	−31.8376			−2.55726
$156$		0			0
$157$	−17.3381	−	12.5969i	−1.38373	−	1.00534i	−0.996520	−	0.0833488i	$-0.973438\pi$
$157$	−17.3381	−	12.5969i	−1.38373	−	1.00534i	−0.387211	−	0.921991i	$-0.626562\pi$
$158$	−5.47436	+	3.97736i	−0.435517	+	0.316421i
$159$		0			0
$160$	4.21797	−	12.9816i	0.333460	−	1.02628i
$161$	20.7025	−	15.0412i	1.63158	−	1.18541i
$162$		0			0
$163$	4.03810	+	12.4280i	0.316288	+	0.973436i	0.975221	+	0.221234i	$0.0710083\pi$
$163$	4.03810	+	12.4280i	0.316288	+	0.973436i	−0.658932	+	0.752202i	$0.728992\pi$
$164$	16.1524			1.26129
$165$		0			0
$166$	3.80708			0.295487
$167$	−3.32513	−	10.2337i	−0.257306	−	0.791907i	−0.993366	−	0.114991i	$-0.963316\pi$
$167$	−3.32513	−	10.2337i	−0.257306	−	0.791907i	0.736060	−	0.676916i	$-0.236684\pi$
$168$		0			0
$169$	10.0417	−	7.29575i	0.772442	−	0.561212i
$170$	−9.44255	+	29.0612i	−0.724211	+	2.22889i
$171$		0			0
$172$	−29.1664	+	21.1907i	−2.22392	+	1.61577i
$173$	−6.35610	−	4.61797i	−0.483245	−	0.351098i	0.319336	−	0.947642i	$-0.396540\pi$
$173$	−6.35610	−	4.61797i	−0.483245	−	0.351098i	−0.802581	+	0.596544i	$0.796540\pi$
$174$		0			0
$175$	−19.3605			−1.46351
$176$	0.199603	+	4.46079i	0.0150457	+	0.336244i
$177$		0			0
$178$	−1.24981	−	3.84653i	−0.0936774	−	0.288309i
$179$	7.25494	+	5.27102i	0.542260	+	0.393975i	0.824924	−	0.565244i	$-0.191218\pi$
$179$	7.25494	+	5.27102i	0.542260	+	0.393975i	−0.282664	+	0.959219i	$0.591218\pi$
$180$		0			0
$181$	1.43316	−	4.41082i	0.106526	−	0.327854i	−0.883560	−	0.468319i	$-0.844860\pi$
$181$	1.43316	−	4.41082i	0.106526	−	0.327854i	0.990086	+	0.140465i	$0.0448599\pi$
$182$	−1.58678	+	4.88361i	−0.117620	+	0.361997i
$183$		0			0
$184$	−25.9157	−	18.8288i	−1.91053	−	1.38808i
$185$	4.81539	+	14.8202i	0.354034	+	1.08961i
$186$		0			0
$187$	0.561592	+	12.5506i	0.0410676	+	0.917789i
$188$	−13.4242			−0.979058
$189$		0			0
$190$	18.5685	+	13.4908i	1.34710	+	0.978725i
$191$	1.48596	−	1.07961i	0.107520	−	0.0781180i	−0.532726	−	0.846288i	$-0.678832\pi$
$191$	1.48596	−	1.07961i	0.107520	−	0.0781180i	0.640246	+	0.768170i	$0.278832\pi$
$192$		0			0
$193$	2.46233	−	7.57827i	0.177242	−	0.545496i	−0.822487	−	0.568785i	$-0.807414\pi$
$193$	2.46233	−	7.57827i	0.177242	−	0.545496i	0.999729	+	0.0232891i	$0.00741381\pi$
$194$	19.6786	−	14.2973i	1.41284	−	1.02649i
$195$		0			0
$196$	1.22739	+	3.77753i	0.0876710	+	0.269824i
$197$	18.5022			1.31823			0.659113	−	0.752044i	$-0.270932\pi$
$197$	18.5022			1.31823			0.659113	+	0.752044i	$0.270932\pi$
$198$		0			0
$199$	−20.8126			−1.47536			−0.737682	−	0.675149i	$-0.764079\pi$
$199$	−20.8126			−1.47536			−0.737682	+	0.675149i	$0.764079\pi$
$200$	7.48927	+	23.0496i	0.529571	+	1.62985i
$201$		0			0
$202$	11.7899	−	8.56586i	0.829535	−	0.602692i
$203$	−2.07614	+	6.38971i	−0.145717	+	0.448470i
$204$		0			0
$205$	12.7503	−	9.26364i	0.890520	−	0.647001i
$206$	−10.3800	−	7.54150i	−0.723208	−	0.525441i
$207$		0			0
$208$	1.03214			0.0715657
$209$	9.09600	+	2.51194i	0.629183	+	0.173754i
$210$		0			0
$211$	5.80605	+	17.8692i	0.399705	+	1.23017i	0.925236	+	0.379391i	$0.123867\pi$
$211$	5.80605	+	17.8692i	0.399705	+	1.23017i	−0.525531	+	0.850774i	$0.676133\pi$
$212$	−17.7929	−	12.9273i	−1.22202	−	0.887848i
$213$		0			0
$214$	6.48313	−	19.9530i	0.443177	−	1.36396i
$215$	−10.8701	+	33.4547i	−0.741333	+	2.28159i
$216$		0			0
$217$	21.3865	+	15.5382i	1.45181	+	1.05480i
$218$	−1.76328	−	5.42682i	−0.119424	−	0.367550i
$219$		0			0
$220$	24.9831	+	31.3384i	1.68436	+	2.11283i
$221$	2.90395			0.195341
$222$		0			0
$223$	8.10997	+	5.89223i	0.543083	+	0.394573i	0.825229	−	0.564798i	$-0.191046\pi$
$223$	8.10997	+	5.89223i	0.543083	+	0.394573i	−0.282145	+	0.959372i	$0.591046\pi$
$224$	−9.16896	+	6.66164i	−0.612627	+	0.445099i
$225$		0			0
$226$	8.31742	−	25.5984i	0.553266	−	1.70278i
$227$	−16.6323	+	12.0840i	−1.10392	+	0.802046i	−0.981696	−	0.190457i	$-0.939003\pi$
$227$	−16.6323	+	12.0840i	−1.10392	+	0.802046i	−0.122226	+	0.992502i	$0.539003\pi$
$228$		0			0
$229$	3.24763	+	9.99517i	0.214609	+	0.660499i	0.999181	+	0.0404614i	$0.0128828\pi$
$229$	3.24763	+	9.99517i	0.214609	+	0.660499i	−0.784572	+	0.620038i	$0.787117\pi$
$230$	−72.4036			−4.77415
$231$		0			0
$232$	8.41038			0.552168
$233$	4.55340	+	14.0139i	0.298303	+	0.918083i	0.982092	+	0.188403i	$0.0603311\pi$
$233$	4.55340	+	14.0139i	0.298303	+	0.918083i	−0.683788	+	0.729680i	$0.739669\pi$
$234$		0			0
$235$	−10.5967	+	7.69894i	−0.691251	+	0.502223i
$236$	1.55419	−	4.78330i	0.101169	−	0.311367i
$237$		0			0
$238$	20.5261	−	14.9131i	1.33051	−	0.966672i
$239$	5.90384	+	4.28939i	0.381888	+	0.277458i	0.762123	−	0.647432i	$-0.224157\pi$
$239$	5.90384	+	4.28939i	0.381888	+	0.277458i	−0.380235	+	0.924890i	$0.624157\pi$
$240$		0			0
$241$	−7.65375			−0.493021			−0.246511	−	0.969140i	$-0.579284\pi$
$241$	−7.65375			−0.493021			−0.246511	+	0.969140i	$0.579284\pi$
$242$	22.1799	+	13.2617i	1.42578	+	0.852496i
$243$		0			0
$244$	0.598008	+	1.84048i	0.0382836	+	0.117825i
$245$	3.13534	+	2.27796i	0.200309	+	0.145533i
$246$		0			0
$247$	0.674036	−	2.07447i	0.0428879	−	0.131995i
$248$	10.2260	−	31.4724i	0.649351	−	1.99850i
$249$		0			0
$250$	11.6857	+	8.49019i	0.739072	+	0.536967i
$251$	−3.51870	−	10.8294i	−0.222098	−	0.683549i	−0.998573	−	0.0534003i	$-0.982994\pi$
$251$	−3.51870	−	10.8294i	−0.222098	−	0.683549i	0.776475	−	0.630148i	$-0.217006\pi$
$252$		0			0
$253$	−27.8717	+	10.4552i	−1.75228	+	0.657313i
$254$	1.79468			0.112608
$255$		0			0
$256$	19.1441	+	13.9090i	1.19650	+	0.869311i
$257$	2.36798	−	1.72044i	0.147711	−	0.107318i	−0.511476	−	0.859298i	$-0.670901\pi$
$257$	2.36798	−	1.72044i	0.147711	−	0.107318i	0.659186	+	0.751980i	$0.270901\pi$
$258$		0			0
$259$	3.99828	−	12.3054i	0.248441	−	0.764623i
$260$	7.49472	−	5.44524i	0.464803	−	0.337699i
$261$		0			0
$262$	−1.00839	−	3.10350i	−0.0622985	−	0.191735i
$263$	27.3188			1.68455			0.842274	−	0.539050i	$-0.181217\pi$
$263$	27.3188			1.68455			0.842274	+	0.539050i	$0.181217\pi$
$264$		0			0
$265$	−21.4592			−1.31823
$266$	−5.88901	−	18.1245i	−0.361079	−	1.11129i
$267$		0			0
$268$	23.1771	−	16.8392i	1.41577	−	1.02861i
$269$	4.31250	−	13.2725i	0.262938	−	0.809240i	−0.729223	−	0.684276i	$-0.760118\pi$
$269$	4.31250	−	13.2725i	0.262938	−	0.809240i	0.992161	−	0.124964i	$-0.0398815\pi$
$270$		0			0
$271$	−10.8526	+	7.88486i	−0.659247	+	0.478971i	−0.866409	−	0.499336i	$-0.833578\pi$
$271$	−10.8526	+	7.88486i	−0.659247	+	0.478971i	0.207161	+	0.978307i	$0.433578\pi$
$272$	−4.12581	−	2.99757i	−0.250164	−	0.181755i
$273$		0			0
$274$	−12.5569			−0.758592
$275$	21.7092	+	5.99518i	1.30911	+	0.361523i
$276$		0			0
$277$	−3.39727	−	10.4557i	−0.204122	−	0.628223i	−0.999748	−	0.0224351i	$-0.992858\pi$
$277$	−3.39727	−	10.4557i	−0.204122	−	0.628223i	0.795626	−	0.605788i	$-0.207142\pi$
$278$	10.0052	+	7.26920i	0.600072	+	0.435978i
$279$		0			0
$280$	10.7972	−	33.2302i	0.645253	−	1.98589i
$281$	−5.23327	+	16.1063i	−0.312191	+	0.960824i	0.664705	+	0.747106i	$0.268557\pi$
$281$	−5.23327	+	16.1063i	−0.312191	+	0.960824i	−0.976895	+	0.213718i	$0.931443\pi$
$282$		0			0
$283$	−1.13907	−	0.827583i	−0.0677107	−	0.0491947i	0.553415	−	0.832906i	$-0.313324\pi$
$283$	−1.13907	−	0.827583i	−0.0677107	−	0.0491947i	−0.621126	+	0.783711i	$0.713324\pi$
$284$	11.0816	+	34.1057i	0.657572	+	2.02380i
$285$		0			0
$286$	3.29154	−	4.98470i	0.194633	−	0.294752i
$287$	−13.0859			−0.772438
$288$		0			0
$289$	2.14518	+	1.55857i	0.126187	+	0.0916804i
$290$	15.3790	−	11.1735i	0.903087	−	0.656131i
$291$		0			0
$292$	−17.8396	+	54.9046i	−1.04398	+	3.21305i
$293$	−23.9129	+	17.3738i	−1.39701	+	1.01499i	−0.401954	+	0.915660i	$0.631669\pi$
$293$	−23.9129	+	17.3738i	−1.39701	+	1.01499i	−0.995055	+	0.0993269i	$0.968331\pi$
$294$		0			0
$295$	−1.51645	−	4.66716i	−0.0882913	−	0.271733i
$296$	−16.1969			−0.941425
$297$		0			0
$298$	35.2023			2.03922
$299$	2.12630	+	6.54408i	0.122967	+	0.378454i
$300$		0			0
$301$	23.6292	−	17.1676i	1.36197	−	0.989526i
$302$	1.96798	−	6.05683i	0.113245	−	0.348532i
$303$		0			0
$304$	−3.09899	+	2.25155i	−0.177739	+	0.129135i
$305$	1.52759	+	1.10986i	0.0874696	+	0.0635504i
$306$		0			0
$307$	4.47267			0.255269			0.127634	−	0.991821i	$-0.459262\pi$
$307$	4.47267			0.255269			0.127634	+	0.991821i	$0.459262\pi$
$308$	−1.48755	−	33.2441i	−0.0847609	−	1.89426i
$309$		0			0
$310$	−23.1132	−	71.1352i	−1.31274	−	4.04021i
$311$	−10.6627	−	7.74687i	−0.604624	−	0.439285i	0.242893	−	0.970053i	$-0.421904\pi$
$311$	−10.6627	−	7.74687i	−0.604624	−	0.439285i	−0.847517	+	0.530768i	$0.821904\pi$
$312$		0			0
$313$	−4.68370	+	14.4149i	−0.264738	+	0.814781i	0.727015	+	0.686621i	$0.240907\pi$
$313$	−4.68370	+	14.4149i	−0.264738	+	0.814781i	−0.991754	+	0.128160i	$0.959093\pi$
$314$	15.5584	−	47.8837i	0.878010	−	2.70224i
$315$		0			0
$316$	−8.20046	−	5.95799i	−0.461312	−	0.335163i
$317$	−0.763061	−	2.34846i	−0.0428578	−	0.131903i	0.927338	−	0.374224i	$-0.122091\pi$
$317$	−0.763061	−	2.34846i	−0.0428578	−	0.131903i	−0.970196	+	0.242322i	$0.922091\pi$
$318$		0			0
$319$	4.30665	−	6.52198i	0.241126	−	0.365161i
$320$	41.3129			2.30946
$321$		0			0
$322$	48.6362	+	35.3363i	2.71039	+	1.96921i
$323$	−8.71912	+	6.33481i	−0.485145	+	0.352479i
$324$		0			0
$325$	1.60871	−	4.95109i	0.0892350	−	0.274637i
$326$	−24.8365	+	18.0448i	−1.37557	+	0.999407i
$327$		0			0
$328$	5.06207	+	15.5794i	0.279506	+	0.860230i
$329$	10.8756			0.599592
$330$		0			0
$331$	−22.5803			−1.24113			−0.620563	−	0.784157i	$-0.713096\pi$
$331$	−22.5803			−1.24113			−0.620563	+	0.784157i	$0.713096\pi$
$332$	1.76230	+	5.42379i	0.0967186	+	0.297669i
$333$		0			0
$334$	20.4513	−	14.8588i	1.11905	−	0.813035i
$335$	8.63791	−	26.5847i	0.471939	−	1.45248i
$336$		0			0
$337$	−24.4347	+	17.7529i	−1.33105	+	0.967061i	−0.331322	+	0.943518i	$0.607495\pi$
$337$	−24.4347	+	17.7529i	−1.33105	+	0.967061i	−0.999723	+	0.0235434i	$0.992505\pi$
$338$	23.5910	+	17.1399i	1.28318	+	0.932286i
$339$		0			0
$340$	−45.7733			−2.48241
$341$	−19.1695	−	24.0458i	−1.03808	−	1.30215i
$342$		0			0
$343$	5.17285	+	15.9204i	0.279307	+	0.859620i
$344$	−29.5795	−	21.4907i	−1.59482	−	1.15870i
$345$		0			0
$346$	5.70365	−	17.5540i	0.306630	−	0.943711i
$347$	4.89583	−	15.0678i	0.262822	−	0.808883i	−0.729365	−	0.684125i	$-0.760184\pi$
$347$	4.89583	−	15.0678i	0.262822	−	0.808883i	0.992187	−	0.124759i	$-0.0398156\pi$
$348$		0			0
$349$	9.12179	+	6.62737i	0.488278	+	0.354755i	0.804522	−	0.593923i	$-0.202422\pi$
$349$	9.12179	+	6.62737i	0.488278	+	0.354755i	−0.316244	+	0.948678i	$0.602422\pi$
$350$	−14.0552	−	43.2574i	−0.751280	−	2.31220i
$351$		0			0
$352$	12.3441	−	4.63053i	0.657945	−	0.246808i
$353$	−14.3301			−0.762714			−0.381357	−	0.924428i	$-0.624543\pi$
$353$	−14.3301			−0.762714			−0.381357	+	0.924428i	$0.624543\pi$
$354$		0			0
$355$	28.3076	+	20.5667i	1.50241	+	1.09157i
$356$	4.90146	−	3.56112i	0.259777	−	0.188739i
$357$		0			0
$358$	−6.51023	+	20.0364i	−0.344076	+	1.05896i
$359$	4.72976	−	3.43637i	0.249627	−	0.181365i	−0.455934	−	0.890013i	$-0.650695\pi$
$359$	4.72976	−	3.43637i	0.249627	−	0.181365i	0.705562	+	0.708649i	$0.250695\pi$
$360$		0			0
$361$	−3.36977	−	10.3711i	−0.177356	−	0.545847i
$362$	10.8956			0.572659
$363$		0			0
$364$	−7.69201			−0.403171
$365$	17.4064	+	53.5715i	0.911094	+	2.80406i
$366$		0			0
$367$	13.0471	−	9.47926i	0.681052	−	0.494813i	−0.192655	−	0.981267i	$-0.561710\pi$
$367$	13.0471	−	9.47926i	0.681052	−	0.494813i	0.873706	+	0.486454i	$0.161710\pi$
$368$	3.73411	−	11.4924i	0.194654	−	0.599083i
$369$		0			0
$370$	−29.6172	+	21.5182i	−1.53973	+	1.11868i
$371$	14.4149	+	10.4730i	0.748385	+	0.543734i
$372$		0			0
$373$	23.4375			1.21355			0.606775	−	0.794874i	$-0.292463\pi$
$373$	23.4375			1.21355			0.606775	+	0.794874i	$0.292463\pi$
$374$	−27.6342	+	10.3661i	−1.42893	+	0.536021i
$375$		0			0
$376$	−4.20704	−	12.9479i	−0.216962	−	0.667739i
$377$	−1.46154	−	1.06187i	−0.0752731	−	0.0546891i
$378$		0			0
$379$	−8.18962	+	25.2051i	−0.420672	+	1.29470i	0.486405	+	0.873733i	$0.338308\pi$
$379$	−8.18962	+	25.2051i	−0.420672	+	1.29470i	−0.907078	+	0.420963i	$0.861692\pi$
$380$	−10.6244	+	32.6987i	−0.545022	+	1.67741i
$381$		0			0
$382$	3.49096	+	2.53633i	0.178613	+	0.129770i
$383$	−2.91381	−	8.96777i	−0.148889	−	0.458232i	0.848602	−	0.529032i	$-0.177445\pi$
$383$	−2.91381	−	8.96777i	−0.148889	−	0.458232i	−0.997491	+	0.0708000i	$0.977445\pi$
$384$		0			0
$385$	−20.2401	−	25.3888i	−1.03153	−	1.29394i
$386$	18.7198			0.952813
$387$		0			0
$388$	29.4780	+	21.4170i	1.49652	+	1.08729i
$389$	14.3627	−	10.4351i	0.728217	−	0.529081i	−0.160782	−	0.986990i	$-0.551401\pi$
$389$	14.3627	−	10.4351i	0.728217	−	0.529081i	0.888999	+	0.457909i	$0.151401\pi$
$390$		0			0
$391$	10.5060	−	32.3343i	0.531314	−	1.63521i
$392$	−3.25887	+	2.36771i	−0.164598	+	0.119587i
$393$		0			0
$394$	13.4321	+	41.3397i	0.676698	+	2.08266i
$395$	−9.89021			−0.497631
$396$		0			0
$397$	−9.96764			−0.500261			−0.250131	−	0.968212i	$-0.580474\pi$
$397$	−9.96764			−0.500261			−0.250131	+	0.968212i	$0.580474\pi$
$398$	−15.1093	−	46.5018i	−0.757363	−	2.33092i
$399$		0			0
$400$	−7.39629	+	5.37372i	−0.369814	+	0.268686i
$401$	7.79432	−	23.9885i	0.389230	−	1.19793i	−0.544135	−	0.838998i	$-0.683142\pi$
$401$	7.79432	−	23.9885i	0.389230	−	1.19793i	0.933365	−	0.358929i	$-0.116858\pi$
$402$		0			0
$403$	−5.75067	+	4.17810i	−0.286461	+	0.208126i
$404$	17.6610	+	12.8315i	0.878668	+	0.638389i
$405$		0			0
$406$	−15.7838			−0.783338
$407$	−8.29384	+	12.5602i	−0.411110	+	0.622584i
$408$		0			0
$409$	−6.55407	−	20.1713i	−0.324078	−	0.997409i	−0.971855	−	0.235579i	$-0.924301\pi$
$409$	−6.55407	−	20.1713i	−0.324078	−	0.997409i	0.647777	−	0.761830i	$-0.275699\pi$
$410$	29.9542	+	21.7630i	1.47933	+	1.07480i
$411$		0			0
$412$	5.93918	−	18.2789i	0.292603	−	0.900538i
$413$	−1.25913	+	3.87520i	−0.0619577	+	0.190686i
$414$		0			0
$415$	4.50173	+	3.27070i	0.220981	+	0.160552i
$416$	−0.941723	−	2.89832i	−0.0461718	−	0.142102i
$417$		0			0
$418$	0.990991	+	22.1469i	0.0484710	+	1.08324i
$419$	−16.7286			−0.817246			−0.408623	−	0.912703i	$-0.633991\pi$
$419$	−16.7286			−0.817246			−0.408623	+	0.912703i	$0.633991\pi$
$420$		0			0
$421$	0.304402	+	0.221161i	0.0148357	+	0.0107787i	0.595178	−	0.803594i	$-0.297081\pi$
$421$	0.304402	+	0.221161i	0.0148357	+	0.0107787i	−0.580343	+	0.814372i	$0.697081\pi$
$422$	−35.7103	+	25.9451i	−1.73835	+	1.26299i
$423$		0			0
$424$	6.89251	−	21.2130i	0.334730	−	1.03019i
$425$	−20.8097	+	15.1191i	−1.00942	+	0.733386i
$426$		0			0
$427$	−0.484477	−	1.49107i	−0.0234455	−	0.0721579i
$428$	31.4273			1.51910
$429$		0			0
$430$	−82.6396			−3.98523
$431$	9.14751	+	28.1532i	0.440620	+	1.35609i	0.887216	+	0.461354i	$0.152636\pi$
$431$	9.14751	+	28.1532i	0.440620	+	1.35609i	−0.446596	+	0.894736i	$0.647364\pi$
$432$		0			0
$433$	14.7149	−	10.6910i	0.707155	−	0.513778i	−0.175100	−	0.984551i	$-0.556025\pi$
$433$	14.7149	−	10.6910i	0.707155	−	0.513778i	0.882255	+	0.470773i	$0.156025\pi$
$434$	−19.1912	+	59.0645i	−0.921207	+	2.83519i
$435$		0			0
$436$	6.91515	−	5.02415i	0.331176	−	0.240613i
$437$	−20.6598	−	15.0102i	−0.988292	−	0.718036i
$438$		0			0
$439$	−35.7900			−1.70816			−0.854081	−	0.520140i	$-0.825880\pi$
$439$	−35.7900			−1.70816			−0.854081	+	0.520140i	$0.825880\pi$
$440$	−22.3971	+	33.9181i	−1.06774	+	1.61698i
$441$		0			0
$442$	2.10819	+	6.48834i	0.100276	+	0.308619i
$443$	24.6012	+	17.8738i	1.16884	+	0.849211i	0.990869	−	0.134825i	$-0.0430471\pi$
$443$	24.6012	+	17.8738i	1.16884	+	0.849211i	0.177970	+	0.984036i	$0.443047\pi$
$444$		0			0
$445$	1.82673	−	5.62210i	0.0865953	−	0.266513i
$446$	−7.27749	+	22.3978i	−0.344599	+	1.06057i
$447$		0			0
$448$	−27.7514	−	20.1626i	−1.31113	−	0.952591i
$449$	3.55921	+	10.9541i	0.167969	+	0.516957i	0.999243	−	0.0389070i	$-0.0123876\pi$
$449$	3.55921	+	10.9541i	0.167969	+	0.516957i	−0.831273	+	0.555864i	$0.812388\pi$
$450$		0			0
$451$	14.6735	+	4.05220i	0.690946	+	0.190811i
$452$	40.3191			1.89645
$453$		0			0
$454$	−39.0741	−	28.3890i	−1.83384	−	1.33236i
$455$	−6.07186	+	4.41147i	−0.284653	+	0.206813i
$456$		0			0
$457$	−8.82439	+	27.1587i	−0.412787	+	1.27043i	0.501428	+	0.865200i	$0.332808\pi$
$457$	−8.82439	+	27.1587i	−0.412787	+	1.27043i	−0.914215	+	0.405229i	$0.867192\pi$
$458$	−19.9746	+	14.5124i	−0.933354	+	0.678121i
$459$		0			0
$460$	−33.5157	−	103.151i	−1.56268	−	4.80942i
$461$	−17.4291			−0.811753			−0.405876	−	0.913928i	$-0.633034\pi$
$461$	−17.4291			−0.811753			−0.405876	+	0.913928i	$0.633034\pi$
$462$		0			0
$463$	−14.3343			−0.666172			−0.333086	−	0.942897i	$-0.608090\pi$
$463$	−14.3343			−0.666172			−0.333086	+	0.942897i	$0.608090\pi$
$464$	0.980386	+	3.01732i	0.0455133	+	0.140075i
$465$		0			0
$466$	−28.0059	+	20.3475i	−1.29735	+	0.942578i
$467$	1.17764	−	3.62441i	0.0544948	−	0.167718i	−0.920105	−	0.391672i	$-0.871897\pi$
$467$	1.17764	−	3.62441i	0.0544948	−	0.167718i	0.974600	+	0.223954i	$0.0718967\pi$
$468$		0			0
$469$	−18.7770	+	13.6423i	−0.867040	+	0.629941i
$470$	−24.8947	−	18.0871i	−1.14831	−	0.834295i
$471$		0			0
$472$	5.10069			0.234778
$473$	−31.8120	+	11.9333i	−1.46272	+	0.548694i
$474$		0			0
$475$	5.97039	+	18.3750i	0.273940	+	0.843101i
$476$	30.7476	+	22.3395i	1.40931	+	1.02393i
$477$		0			0
$478$	−5.29782	+	16.3050i	−0.242317	+	0.745774i
$479$	6.45103	−	19.8542i	0.294755	−	0.907163i	−0.688549	−	0.725190i	$-0.741752\pi$
$479$	6.45103	−	19.8542i	0.294755	−	0.907163i	0.983304	−	0.181972i	$-0.0582482\pi$
$480$		0			0
$481$	2.81466	+	2.04497i	0.128338	+	0.0932428i
$482$	−5.55641	−	17.1009i	−0.253088	−	0.778923i
$483$		0			0
$484$	−8.62637	+	37.7377i	−0.392108	+	1.71535i
$485$	35.5521			1.61434
$486$		0			0
$487$	−0.0558552	−	0.0405812i	−0.00253104	−	0.00183891i	0.586519	−	0.809935i	$-0.300498\pi$
$487$	−0.0558552	−	0.0405812i	−0.00253104	−	0.00183891i	−0.589050	+	0.808097i	$0.700498\pi$
$488$	−1.58778	+	1.15359i	−0.0718753	+	0.0522205i
$489$		0			0
$490$	−2.81350	+	8.65906i	−0.127101	+	0.391176i
$491$	27.8350	−	20.2233i	1.25618	−	0.912667i	0.257614	−	0.966248i	$-0.417064\pi$
$491$	27.8350	−	20.2233i	1.25618	−	0.912667i	0.998563	+	0.0535812i	$0.0170636\pi$
$492$		0			0
$493$	2.75835	+	8.48933i	0.124230	+	0.382340i
$494$	5.12435			0.230555
$495$		0			0
$496$	12.4831			0.560508
$497$	−8.97778	−	27.6308i	−0.402709	−	1.23941i
$498$		0			0
$499$	−26.0473	+	18.9245i	−1.16604	+	0.847176i	−0.990529	−	0.137302i	$-0.956157\pi$
$499$	−26.0473	+	18.9245i	−1.16604	+	0.847176i	−0.175509	+	0.984478i	$0.556157\pi$
$500$	−6.68631	+	20.5783i	−0.299021	+	0.920291i
$501$		0			0
$502$	21.6419	−	15.7238i	0.965925	−	0.701786i
$503$	15.4970	+	11.2592i	0.690976	+	0.502023i	0.876981	−	0.480525i	$-0.159554\pi$
$503$	15.4970	+	11.2592i	0.690976	+	0.502023i	−0.186005	+	0.982549i	$0.559554\pi$
$504$		0			0
$505$	21.3001			0.947844
$506$	−43.5943	−	54.6838i	−1.93800	−	2.43099i
$507$		0			0
$508$	0.830759	+	2.55681i	0.0368590	+	0.113440i
$509$	−15.9370	−	11.5789i	−0.706395	−	0.513226i	0.175614	−	0.984459i	$-0.443809\pi$
$509$	−15.9370	−	11.5789i	−0.706395	−	0.513226i	−0.882009	+	0.471233i	$0.843809\pi$
$510$		0			0
$511$	14.4528	−	44.4811i	0.639353	−	1.96773i
$512$	−4.62350	+	14.2297i	−0.204332	+	0.628869i
$513$		0			0
$514$	5.56309	+	4.04182i	0.245377	+	0.178277i
$515$	−5.79497	−	17.8351i	−0.255357	−	0.785908i
$516$		0			0
$517$	−12.1950	−	3.36775i	−0.536335	−	0.148113i
$518$	30.3968			1.33556
$519$		0			0
$520$	7.60086	+	5.52235i	0.333320	+	0.242171i
$521$	7.93700	−	5.76657i	0.347726	−	0.252638i	−0.400188	−	0.916433i	$-0.631055\pi$
$521$	7.93700	−	5.76657i	0.347726	−	0.252638i	0.747914	+	0.663795i	$0.231055\pi$
$522$		0			0
$523$	12.0026	−	36.9401i	0.524836	−	1.61528i	−0.239805	−	0.970821i	$-0.577083\pi$
$523$	12.0026	−	36.9401i	0.524836	−	1.61528i	0.764641	−	0.644457i	$-0.222917\pi$
$524$	3.95466	−	2.87323i	0.172760	−	0.125517i
$525$		0			0
$526$	19.8327	+	61.0387i	0.864746	+	2.66141i
$527$	35.1216			1.52992
$528$		0			0
$529$	57.5583			2.50253
$530$	−15.5788	−	47.9465i	−0.676698	−	2.08266i
$531$		0			0
$532$	23.0953	−	16.7797i	1.00131	−	0.727492i
$533$	1.08734	−	3.34649i	0.0470979	−	0.144952i
$534$		0			0
$535$	24.8079	−	18.0240i	1.07254	−	0.779244i
$536$	23.5053	+	17.0776i	1.01528	+	0.737641i
$537$		0			0
$538$	32.7857			1.41349
$539$	0.167331	+	3.73956i	0.00720748	+	0.161074i
$540$		0			0
$541$	0.621273	+	1.91208i	0.0267106	+	0.0822068i	0.963523	−	0.267625i	$-0.0862388\pi$
$541$	0.621273	+	1.91208i	0.0267106	+	0.0822068i	−0.936813	+	0.349832i	$0.886239\pi$
$542$	−25.4959	−	18.5239i	−1.09514	−	0.795669i
$543$		0			0
$544$	−4.65305	+	14.3206i	−0.199498	+	0.613991i
$545$	2.57722	−	7.93186i	0.110396	−	0.339764i
$546$		0			0
$547$	14.3470	+	10.4237i	0.613435	+	0.445686i	0.850622	−	0.525777i	$-0.176226\pi$
$547$	14.3470	+	10.4237i	0.613435	+	0.445686i	−0.237187	+	0.971464i	$0.576226\pi$
$548$	−5.81261	−	17.8894i	−0.248302	−	0.764196i
$549$		0			0
$550$	2.36517	+	52.8575i	0.100851	+	2.25385i
$551$	6.70469			0.285629
$552$		0			0
$553$	6.64362	+	4.82687i	0.282515	+	0.205260i
$554$	20.8950	−	15.1811i	0.887744	−	0.644984i
$555$		0			0
$556$	−5.72474	+	17.6189i	−0.242783	+	0.747209i
$557$	4.47338	−	3.25010i	0.189543	−	0.137711i	−0.488967	−	0.872302i	$-0.662626\pi$
$557$	4.47338	−	3.25010i	0.189543	−	0.137711i	0.678510	+	0.734591i	$0.262626\pi$
$558$		0			0
$559$	2.42690	+	7.46924i	0.102647	+	0.315915i
$560$	13.1803			0.556970
$561$		0			0
$562$	−39.7858			−1.67826
$563$	−3.19267	−	9.82603i	−0.134555	−	0.414118i	0.860966	−	0.508663i	$-0.169860\pi$
$563$	−3.19267	−	9.82603i	−0.134555	−	0.414118i	−0.995521	+	0.0945456i	$0.969860\pi$
$564$		0			0
$565$	31.8268	−	23.1236i	1.33897	−	0.972815i
$566$	1.02215	−	3.14584i	0.0429640	−	0.132230i
$567$		0			0
$568$	−29.4229	+	21.3770i	−1.23456	+	0.896958i
$569$	−25.6851	−	18.6613i	−1.07678	−	0.782324i	−0.0996583	−	0.995022i	$-0.531775\pi$
$569$	−25.6851	−	18.6613i	−1.07678	−	0.782324i	−0.977118	+	0.212698i	$0.931775\pi$
$570$		0			0
$571$	12.6273			0.528435			0.264217	−	0.964463i	$-0.414886\pi$
$571$	12.6273			0.528435			0.264217	+	0.964463i	$0.414886\pi$
$572$	8.62517	+	2.38191i	0.360636	+	0.0995927i
$573$		0			0
$574$	−9.50002	−	29.2381i	−0.396523	−	1.22037i
$575$	−49.3082	−	35.8245i	−2.05630	−	1.49399i
$576$		0			0
$577$	−10.7802	+	33.1782i	−0.448788	+	1.38123i	0.429488	+	0.903072i	$0.358694\pi$
$577$	−10.7802	+	33.1782i	−0.448788	+	1.38123i	−0.878276	+	0.478154i	$0.841306\pi$
$578$	−1.92498	+	5.92449i	−0.0800687	+	0.246426i
$579$		0			0
$580$	23.0374	+	16.7377i	0.956576	+	0.694993i
$581$	−1.42773	−	4.39410i	−0.0592322	−	0.182298i
$582$		0			0
$583$	−12.9206	−	16.2073i	−0.535116	−	0.671239i
$584$	−58.5477			−2.42272
$585$		0			0
$586$	−56.1786	−	40.8161i	−2.32072	−	1.68610i
$587$	24.1389	−	17.5379i	0.996319	−	0.723868i	0.0350231	−	0.999387i	$-0.488850\pi$
$587$	24.1389	−	17.5379i	0.996319	−	0.723868i	0.961296	+	0.275518i	$0.0888495\pi$
$588$		0			0
$589$	8.15209	−	25.0895i	0.335901	−	1.03380i
$590$	9.32699	−	6.77646i	0.383986	−	0.278982i
$591$		0			0
$592$	−1.88805	−	5.81082i	−0.0775983	−	0.238823i
$593$	−25.1802			−1.03403			−0.517014	−	0.855977i	$-0.672956\pi$
$593$	−25.1802			−1.03403			−0.517014	+	0.855977i	$0.672956\pi$
$594$		0			0
$595$	37.0833			1.52027
$596$	16.2952	+	50.1514i	0.667476	+	2.05428i
$597$		0			0
$598$	−13.0779	+	9.50165i	−0.534795	+	0.388551i
$599$	−2.10006	+	6.46331i	−0.0858060	+	0.264084i	−0.984749	−	0.173982i	$-0.944336\pi$
$599$	−2.10006	+	6.46331i	−0.0858060	+	0.264084i	0.898943	+	0.438066i	$0.144336\pi$
$600$		0			0
$601$	−13.2289	+	9.61137i	−0.539619	+	0.392056i	−0.823944	−	0.566672i	$-0.808231\pi$
$601$	−13.2289	+	9.61137i	−0.539619	+	0.392056i	0.284325	+	0.958728i	$0.408231\pi$
$602$	55.5121	+	40.3319i	2.26250	+	1.64380i
$603$		0			0
$604$	9.53992			0.388174
$605$	14.8337	+	34.7365i	0.603074	+	1.41224i
$606$		0			0
$607$	−2.84286	−	8.74942i	−0.115388	−	0.355128i	0.876640	−	0.481147i	$-0.159780\pi$
$607$	−2.84286	−	8.74942i	−0.115388	−	0.355128i	−0.992028	+	0.126019i	$0.959780\pi$
$608$	9.15007	+	6.64791i	0.371084	+	0.269608i
$609$		0			0
$610$	−1.37079	+	4.21885i	−0.0555015	+	0.170816i
$611$	−0.903679	+	2.78124i	−0.0365590	+	0.112517i
$612$		0			0
$613$	−27.3588	−	19.8773i	−1.10501	−	0.802837i	−0.123140	−	0.992389i	$-0.539296\pi$
$613$	−27.3588	−	19.8773i	−1.10501	−	0.802837i	−0.981871	+	0.189552i	$0.939296\pi$
$614$	3.24704	+	9.99335i	0.131040	+	0.403299i
$615$		0			0
$616$	31.5985	−	11.8532i	1.27314	−	0.477581i
$617$	−0.912580			−0.0367391			−0.0183695	−	0.999831i	$-0.505848\pi$
$617$	−0.912580			−0.0367391			−0.0183695	+	0.999831i	$0.505848\pi$
$618$		0			0
$619$	−7.47637	−	5.43190i	−0.300501	−	0.218326i	0.427309	−	0.904106i	$-0.359462\pi$
$619$	−7.47637	−	5.43190i	−0.300501	−	0.218326i	−0.727810	+	0.685779i	$0.759462\pi$
$620$	90.6444	−	65.8570i	3.64037	−	2.64488i
$621$		0			0
$622$	9.56815	−	29.4477i	0.383648	−	1.18075i
$623$	−3.97092	+	2.88504i	−0.159092	+	0.115587i
$624$		0			0
$625$	−3.96806	−	12.2124i	−0.158723	−	0.488498i
$626$	−35.6077			−1.42317
$627$		0			0
$628$	75.4201			3.00959
$629$	−5.31209	−	16.3489i	−0.211807	−	0.651875i
$630$		0			0
$631$	2.28995	−	1.66374i	0.0911614	−	0.0662326i	−0.541271	−	0.840848i	$-0.682057\pi$
$631$	2.28995	−	1.66374i	0.0911614	−	0.0662326i	0.632432	+	0.774616i	$0.282057\pi$
$632$	3.17666	−	9.77675i	0.126361	−	0.388898i
$633$		0			0
$634$	4.69324	−	3.40984i	0.186392	−	0.135422i
$635$	2.12214	+	1.54183i	0.0842148	+	0.0611856i
$636$		0			0
$637$	0.865260			0.0342828
$638$	17.6987	+	4.88763i	0.700696	+	0.193503i
$639$		0			0
$640$	21.5561	+	66.3427i	0.852078	+	2.62243i
$641$	6.00148	+	4.36033i	0.237044	+	0.172223i	0.699965	−	0.714177i	$-0.253199\pi$
$641$	6.00148	+	4.36033i	0.237044	+	0.172223i	−0.462921	+	0.886399i	$0.653199\pi$
$642$		0			0
$643$	−7.48866	+	23.0477i	−0.295324	+	0.908914i	0.687788	+	0.725911i	$0.258582\pi$
$643$	−7.48866	+	23.0477i	−0.295324	+	0.908914i	−0.983112	+	0.183003i	$0.941418\pi$
$644$	−27.8285	+	85.6472i	−1.09660	+	3.37497i
$645$		0			0
$646$	−20.4838	−	14.8824i	−0.805924	−	0.585538i
$647$	−0.521170	−	1.60400i	−0.0204893	−	0.0630596i	0.940289	−	0.340377i	$-0.110555\pi$
$647$	−0.521170	−	1.60400i	−0.0204893	−	0.0630596i	−0.960778	+	0.277317i	$0.910555\pi$
$648$		0			0
$649$	2.61188	−	3.95542i	0.102525	−	0.155264i
$650$	12.2302			0.479706
$651$		0			0
$652$	−37.2045	−	27.0306i	−1.45704	−	1.05860i
$653$	−2.88540	+	2.09636i	−0.112914	+	0.0820371i	−0.642809	−	0.766026i	$-0.722231\pi$
$653$	−2.88540	+	2.09636i	−0.112914	+	0.0820371i	0.529895	+	0.848063i	$0.322231\pi$
$654$		0			0
$655$	1.47387	−	4.53610i	0.0575887	−	0.177240i
$656$	−4.99922	+	3.63215i	−0.195187	+	0.141811i
$657$		0			0
$658$	7.89539	+	24.2995i	0.307794	+	0.947294i
$659$	4.48959			0.174889			0.0874447	−	0.996169i	$-0.472130\pi$
$659$	4.48959			0.174889			0.0874447	+	0.996169i	$0.472130\pi$
$660$		0			0
$661$	26.7588			1.04080			0.520398	−	0.853924i	$-0.325784\pi$
$661$	26.7588			1.04080			0.520398	+	0.853924i	$0.325784\pi$
$662$	−16.3927	−	50.4515i	−0.637119	−	1.96085i
$663$		0			0
$664$	−4.67909	+	3.39956i	−0.181584	+	0.131929i
$665$	8.60741	−	26.4909i	0.333781	−	1.02727i
$666$		0			0
$667$	−17.1111	+	12.4319i	−0.662545	+	0.481367i
$668$	30.6356	+	22.2581i	1.18533	+	0.861191i
$669$		0			0
$670$	65.6695			2.53704
$671$	0.0815269	+	1.82198i	0.00314731	+	0.0703368i
$672$		0			0
$673$	2.03719	+	6.26983i	0.0785279	+	0.241684i	0.982612	−	0.185670i	$-0.0594457\pi$
$673$	2.03719	+	6.26983i	0.0785279	+	0.241684i	−0.904084	+	0.427354i	$0.859446\pi$
$674$	−57.4044	−	41.7068i	−2.21114	−	1.60648i
$675$		0			0
$676$	−13.4982	+	41.5433i	−0.519162	+	1.59782i
$677$	9.38490	−	28.8837i	0.360691	−	1.11009i	−0.591945	−	0.805979i	$-0.701640\pi$
$677$	9.38490	−	28.8837i	0.360691	−	1.11009i	0.952636	−	0.304114i	$-0.0983604\pi$
$678$		0			0
$679$	−23.8817	−	17.3511i	−0.916495	−	0.665873i
$680$	−14.3450	−	44.1495i	−0.550107	−	1.69306i
$681$		0			0
$682$	39.8093	−	60.2871i	1.52438	−	2.30851i
$683$	−16.3164			−0.624328			−0.312164	−	0.950028i	$-0.601054\pi$
$683$	−16.3164			−0.624328			−0.312164	+	0.950028i	$0.601054\pi$
$684$		0			0
$685$	−14.8481	−	10.7878i	−0.567317	−	0.412180i
$686$	−31.8158	+	23.1155i	−1.21473	+	0.882555i
$687$		0			0
$688$	4.26201	−	13.1171i	0.162488	−	0.500085i
$689$	−3.87606	+	2.81612i	−0.147666	+	0.107286i
$690$		0			0
$691$	1.61852	+	4.98128i	0.0615713	+	0.189497i	0.977111	−	0.212731i	$-0.0682359\pi$
$691$	1.61852	+	4.98128i	0.0615713	+	0.189497i	−0.915539	+	0.402228i	$0.868236\pi$
$692$	27.6488			1.05105
$693$		0			0
$694$	37.2205			1.41287
$695$	5.58574	+	17.1911i	0.211879	+	0.652097i
$696$		0			0
$697$	−14.0655	+	10.2192i	−0.532768	+	0.387079i
$698$	−8.18545	+	25.1922i	−0.309824	+	0.953539i
$699$		0			0
$700$	55.1209	−	40.0477i	2.08338	−	1.51366i
$701$	−27.8779	−	20.2545i	−1.05293	−	0.765001i	−0.0801656	−	0.996782i	$-0.525545\pi$
$701$	−27.8779	−	20.2545i	−1.05293	−	0.765001i	−0.972768	+	0.231780i	$0.925545\pi$
$702$		0			0
$703$	−12.9120			−0.486987
$704$	24.8745	+	31.2021i	0.937493	+	1.17597i
$705$		0			0
$706$	−10.4033	−	32.0179i	−0.391532	−	1.20501i
$707$	−14.3081	−	10.3954i	−0.538111	−	0.390961i
$708$		0			0
$709$	2.13886	−	6.58272i	0.0803264	−	0.247219i	−0.902826	−	0.430006i	$-0.858512\pi$
$709$	2.13886	−	6.58272i	0.0803264	−	0.247219i	0.983153	+	0.182786i	$0.0585116\pi$
$710$	−25.4018	+	78.1788i	−0.953314	+	2.93400i
$711$		0			0
$712$	4.97087	+	3.61155i	0.186291	+	0.135348i
$713$	25.7164	+	79.1470i	0.963087	+	2.96408i
$714$		0			0
$715$	8.17453	−	3.06643i	0.305710	−	0.114678i
$716$	−31.5587			−1.17940
$717$		0			0
$718$	11.1116	+	8.07306i	0.414682	+	0.301284i
$719$	−41.1498	+	29.8971i	−1.53463	+	1.11497i	−0.581036	+	0.813878i	$0.697352\pi$
$719$	−41.1498	+	29.8971i	−1.53463	+	1.11497i	−0.953594	+	0.301096i	$0.902648\pi$
$720$		0			0
$721$	−4.81164	+	14.8087i	−0.179195	+	0.551505i
$722$	20.7259	−	15.0583i	0.771339	−	0.560410i
$723$		0			0
$724$	5.04357	+	15.5225i	0.187443	+	0.576890i
$725$	16.0019			0.594297
$726$		0			0
$727$	−20.5953			−0.763837			−0.381919	−	0.924196i	$-0.624737\pi$
$727$	−20.5953			−0.763837			−0.381919	+	0.924196i	$0.624737\pi$
$728$	−2.41062	−	7.41913i	−0.0893436	−	0.274971i
$729$		0			0
$730$	−107.059	+	77.7828i	−3.96243	+	2.87887i
$731$	11.9913	−	36.9055i	0.443515	−	1.36500i
$732$		0			0
$733$	31.5147	−	22.8968i	1.16402	−	0.845712i	0.173741	−	0.984791i	$-0.444414\pi$
$733$	31.5147	−	22.8968i	1.16402	−	0.845712i	0.990281	+	0.139080i	$0.0444145\pi$
$734$	30.6514	+	22.2696i	1.13137	+	0.821985i
$735$		0			0
$736$	−35.6786			−1.31513
$737$	25.2794	−	9.48280i	0.931178	−	0.349303i
$738$		0			0
$739$	5.63685	+	17.3485i	0.207355	+	0.638173i	0.999608	+	0.0279809i	$0.00890777\pi$
$739$	5.63685	+	17.3485i	0.207355	+	0.638173i	−0.792253	+	0.610192i	$0.791092\pi$
$740$	−44.3659	−	32.2337i	−1.63092	−	1.18494i
$741$		0			0
$742$	−12.9352	+	39.8106i	−0.474868	+	1.46149i
$743$	−6.89474	+	21.2198i	−0.252944	+	0.778480i	0.741284	+	0.671191i	$0.234217\pi$
$743$	−6.89474	+	21.2198i	−0.252944	+	0.778480i	−0.994228	+	0.107289i	$0.965783\pi$
$744$		0			0
$745$	41.6255	+	30.2427i	1.52504	+	1.10801i
$746$	17.0150	+	52.3668i	0.622963	+	1.91728i
$747$		0			0
$748$	−27.5601	−	34.5709i	−1.00770	−	1.26404i
$749$	−25.4609			−0.930321
$750$		0			0
$751$	10.6590	+	7.74418i	0.388951	+	0.282589i	0.765025	−	0.644000i	$-0.222726\pi$
$751$	10.6590	+	7.74418i	0.388951	+	0.282589i	−0.376075	+	0.926589i	$0.622726\pi$
$752$	4.15481	−	3.01865i	0.151510	−	0.110079i
$753$		0			0
$754$	1.31151	−	4.03643i	0.0477625	−	0.146998i
$755$	7.53055	−	5.47127i	0.274065	−	0.199120i
$756$		0			0
$757$	−13.0098	−	40.0402i	−0.472851	−	1.45529i	−0.848834	−	0.528659i	$-0.822695\pi$
$757$	−13.0098	−	40.0402i	−0.472851	−	1.45529i	0.375983	−	0.926627i	$-0.377305\pi$
$758$	−62.2614			−2.26144
$759$		0			0
$760$	−34.8683			−1.26481
$761$	1.00773	+	3.10146i	0.0365300	+	0.112428i	0.967659	−	0.252263i	$-0.0811747\pi$
$761$	1.00773	+	3.10146i	0.0365300	+	0.112428i	−0.931129	+	0.364691i	$0.881175\pi$
$762$		0			0
$763$	−5.60232	+	4.07032i	−0.202818	+	0.147356i
$764$	−1.99744	+	6.14749i	−0.0722649	+	0.222409i
$765$		0			0
$766$	17.9215	−	13.0207i	0.647529	−	0.470457i
$767$	−0.886388	−	0.643999i	−0.0320056	−	0.0232534i
$768$		0			0
$769$	−38.6954			−1.39539			−0.697696	−	0.716394i	$-0.745791\pi$
$769$	−38.6954			−1.39539			−0.697696	+	0.716394i	$0.745791\pi$
$770$	42.0328	−	63.6544i	1.51476	−	2.29395i
$771$		0			0
$772$	8.66540	+	26.6694i	0.311875	+	0.959851i
$773$	−19.1356	−	13.9028i	−0.688261	−	0.500051i	0.187827	−	0.982202i	$-0.439855\pi$
$773$	−19.1356	−	13.9028i	−0.688261	−	0.500051i	−0.876088	+	0.482152i	$0.839855\pi$
$774$		0			0
$775$	19.4564	−	59.8806i	0.698894	−	2.15098i
$776$	−11.4191	+	35.1443i	−0.409921	+	1.26161i
$777$		0			0
$778$	33.7422	+	24.5152i	1.20972	+	0.878911i
$779$	4.03544	+	12.4198i	0.144585	+	0.444986i
$780$		0			0
$781$	1.51076	+	33.7629i	0.0540593	+	1.20813i
$782$	79.8720			2.85622
$783$		0			0
$784$	−1.22932	−	0.893155i	−0.0439044	−	0.0318984i
$785$	59.5346	−	43.2544i	2.12488	−	1.54382i
$786$		0			0
$787$	−1.03005	+	3.17018i	−0.0367174	+	0.113005i	−0.967735	−	0.251969i	$-0.918922\pi$
$787$	−1.03005	+	3.17018i	−0.0367174	+	0.113005i	0.931018	+	0.364973i	$0.118922\pi$
$788$	−52.6773	+	38.2723i	−1.87655	+	1.36339i
$789$		0			0
$790$	−7.18002	−	22.0978i	−0.255454	−	0.786205i
$791$	−32.6646			−1.16142
$792$		0			0
$793$	0.421570			0.0149704
$794$	−7.23623	−	22.2708i	−0.256804	−	0.790362i
$795$		0			0
$796$	59.2551	−	43.0514i	2.10024	−	1.52592i
$797$	−14.8960	+	45.8452i	−0.527644	+	1.62392i	0.231383	+	0.972863i	$0.425675\pi$
$797$	−14.8960	+	45.8452i	−0.527644	+	1.62392i	−0.759027	+	0.651059i	$0.774325\pi$
$798$		0			0
$799$	11.6897	−	8.49307i	0.413552	−	0.300463i
$800$	21.8382	+	15.8664i	0.772098	+	0.560962i
$801$		0			0
$802$	59.2562			2.09241
$803$	−29.9802	+	45.4019i	−1.05798	+	1.60220i
$804$		0			0
$805$	27.1528	+	83.5676i	0.957009	+	2.94537i
$806$	−13.5100	−	9.81560i	−0.475870	−	0.345740i
$807$		0			0
$808$	−6.84144	+	21.0558i	−0.240681	+	0.740740i
$809$	−7.39099	+	22.7471i	−0.259854	+	0.799747i	0.732981	+	0.680249i	$0.238128\pi$
$809$	−7.39099	+	22.7471i	−0.259854	+	0.799747i	−0.992834	+	0.119498i	$0.961872\pi$
$810$		0			0
$811$	41.0406	+	29.8177i	1.44113	+	1.04704i	0.987805	+	0.155697i	$0.0497622\pi$
$811$	41.0406	+	29.8177i	1.44113	+	1.04704i	0.453325	+	0.891345i	$0.350238\pi$
$812$	−7.30634	−	22.4866i	−0.256402	−	0.789125i
$813$		0			0
$814$	−34.0844	−	9.41271i	−1.19466	−	0.329915i
$815$	−44.8706			−1.57175
$816$		0			0
$817$	−23.5805	−	17.1323i	−0.824979	−	0.599382i
$818$	40.3110	−	29.2877i	1.40944	−	1.02402i
$819$		0			0
$820$	−17.1391	+	52.7487i	−0.598523	+	1.84207i
$821$	35.0446	−	25.4614i	1.22306	−	0.888609i	0.226714	−	0.973961i	$-0.427202\pi$
$821$	35.0446	−	25.4614i	1.22306	−	0.888609i	0.996351	+	0.0853527i	$0.0272017\pi$
$822$		0			0
$823$	−15.4672	−	47.6030i	−0.539152	−	1.65934i	−0.734504	−	0.678605i	$-0.762585\pi$
$823$	−15.4672	−	47.6030i	−0.539152	−	1.65934i	0.195352	−	0.980733i	$-0.437415\pi$
$824$	19.4918			0.679029
$825$		0			0
$826$	−9.57251			−0.333070
$827$	10.4337	+	32.1115i	0.362814	+	1.11663i	0.951339	+	0.308147i	$0.0997089\pi$
$827$	10.4337	+	32.1115i	0.362814	+	1.11663i	−0.588525	+	0.808479i	$0.700291\pi$
$828$		0			0
$829$	−4.79185	+	3.48148i	−0.166428	+	0.120917i	−0.667882	−	0.744268i	$-0.732799\pi$
$829$	−4.79185	+	3.48148i	−0.166428	+	0.120917i	0.501454	+	0.865184i	$0.332799\pi$
$830$	−4.03963	+	12.4327i	−0.140218	+	0.431546i
$831$		0			0
$832$	7.46213	−	5.42156i	0.258703	−	0.187959i
$833$	−3.45874	−	2.51292i	−0.119838	−	0.0870677i
$834$		0			0
$835$	36.9483			1.27865
$836$	−31.0931	+	11.6636i	−1.07538	+	0.403395i
$837$		0			0
$838$	−12.1445	−	37.3770i	−0.419525	−	1.29117i
$839$	21.9803	+	15.9696i	0.758844	+	0.551333i	0.898556	−	0.438860i	$-0.144617\pi$
$839$	21.9803	+	15.9696i	0.758844	+	0.551333i	−0.139711	+	0.990192i	$0.544617\pi$
$840$		0			0
$841$	−7.24551	+	22.2994i	−0.249845	+	0.768944i
$842$	−0.273156	+	0.840687i	−0.00941357	+	0.0289720i
$843$		0			0
$844$	−53.4933	−	38.8651i	−1.84131	−	1.33779i
$845$	13.1705	+	40.5345i	0.453078	+	1.39443i
$846$		0			0
$847$	6.98867	−	30.5733i	0.240133	−	1.05051i
$848$	8.41385			0.288933
$849$		0			0
$850$	−48.8882	−	35.5194i	−1.67685	−	1.21830i
$851$	32.9529	−	23.9417i	1.12961	−	0.820711i
$852$		0			0
$853$	−14.1332	+	43.4974i	−0.483910	+	1.48932i	0.349644	+	0.936883i	$0.386303\pi$
$853$	−14.1332	+	43.4974i	−0.483910	+	1.48932i	−0.833554	+	0.552439i	$0.813697\pi$
$854$	2.97980	−	2.16495i	0.101967	−	0.0740830i
$855$		0			0
$856$	9.84911	+	30.3124i	0.336635	+	1.03606i
$857$	35.5609			1.21474			0.607368	−	0.794421i	$-0.292225\pi$
$857$	35.5609			1.21474			0.607368	+	0.794421i	$0.292225\pi$
$858$		0			0
$859$	4.32361			0.147520			0.0737598	−	0.997276i	$-0.476500\pi$
$859$	4.32361			0.147520			0.0737598	+	0.997276i	$0.476500\pi$
$860$	−38.2539	−	117.733i	−1.30445	−	4.01467i
$861$		0			0
$862$	−56.2621	+	40.8768i	−1.91630	+	1.39227i
$863$	−12.9538	+	39.8676i	−0.440952	+	1.35711i	0.445911	+	0.895077i	$0.352880\pi$
$863$	−12.9538	+	39.8676i	−0.440952	+	1.35711i	−0.886863	+	0.462033i	$0.847120\pi$
$864$		0			0
$865$	21.8252	−	15.8569i	0.742079	−	0.539152i
$866$	34.5697	+	25.1164i	1.17473	+	0.853490i
$867$		0			0
$868$	−93.0304			−3.15766
$869$	−5.95490	−	7.46972i	−0.202006	−	0.253393i
$870$		0			0
$871$	−1.92854	−	5.93543i	−0.0653461	−	0.201115i
$872$	7.01308	+	5.09530i	0.237493	+	0.172549i
$873$		0			0
$874$	18.5391	−	57.0575i	0.627094	−	1.93000i
$875$	5.41692	−	16.6716i	0.183125	−	0.563602i
$876$		0			0
$877$	−29.8521	−	21.6888i	−1.00803	−	0.732380i	−0.0442387	−	0.999021i	$-0.514086\pi$
$877$	−29.8521	−	21.6888i	−1.00803	−	0.732380i	−0.963796	+	0.266641i	$0.914086\pi$
$878$	−25.9825	−	79.9660i	−0.876868	−	2.69872i
$879$		0			0
$880$	−14.7793	−	4.08143i	−0.498210	−	0.137585i
$881$	6.36892			0.214574			0.107287	−	0.994228i	$-0.465784\pi$
$881$	6.36892			0.214574			0.107287	+	0.994228i	$0.465784\pi$
$882$		0			0
$883$	−20.5545	−	14.9337i	−0.691714	−	0.502560i	0.185509	−	0.982643i	$-0.440607\pi$
$883$	−20.5545	−	14.9337i	−0.691714	−	0.502560i	−0.877223	+	0.480083i	$0.840607\pi$
$884$	−8.26780	+	6.00691i	−0.278076	+	0.202034i
$885$		0			0
$886$	−22.0759	+	67.9427i	−0.741655	+	2.28258i
$887$	36.1213	−	26.2437i	1.21284	−	0.881176i	0.217350	−	0.976094i	$-0.430259\pi$
$887$	36.1213	−	26.2437i	1.21284	−	0.881176i	0.995485	+	0.0949174i	$0.0302587\pi$
$888$		0			0
$889$	−0.673041	−	2.07141i	−0.0225731	−	0.0694727i
$890$	13.8877			0.465516
$891$		0			0
$892$	−35.2780			−1.18120
$893$	−3.35382	−	10.3220i	−0.112231	−	0.345413i
$894$		0			0
$895$	−24.9116	+	18.0993i	−0.832703	+	0.604994i
$896$	17.8983	−	55.0852i	0.597939	−	1.84027i
$897$		0			0
$898$	−21.8910	+	15.9048i	−0.730514	+	0.530749i
$899$	−17.6765	−	12.8427i	−0.589544	−	0.428329i
$900$		0			0
$901$	23.6727			0.788651
$902$	1.59864	+	35.7269i	0.0532290	+	1.18957i
$903$		0			0
$904$	12.6357	+	38.8888i	0.420259	+	1.29342i
$905$	12.8836	+	9.36050i	0.428266	+	0.311154i
$906$		0			0
$907$	12.5572	−	38.6471i	0.416956	−	1.28326i	−0.493534	−	0.869726i	$-0.664295\pi$
$907$	12.5572	−	38.6471i	0.416956	−	1.28326i	0.910490	−	0.413531i	$-0.135705\pi$
$908$	22.3573	−	68.8086i	0.741952	−	2.28349i
$909$		0			0
$910$	−14.2646	−	10.3638i	−0.472867	−	0.343558i
$911$	0.990986	+	3.04994i	0.0328328	+	0.101049i	0.966130	−	0.258056i	$-0.0830819\pi$
$911$	0.990986	+	3.04994i	0.0328328	+	0.101049i	−0.933297	+	0.359105i	$0.883082\pi$
$912$		0			0
$913$	0.240255	+	5.36928i	0.00795129	+	0.177697i
$914$	−67.0872			−2.21905
$915$		0			0
$916$	−29.9216	−	21.7393i	−0.988636	−	0.718286i
$917$	−3.20387	+	2.32775i	−0.105801	+	0.0768690i
$918$		0			0
$919$	3.00135	−	9.23720i	0.0990054	−	0.304707i	−0.889271	−	0.457380i	$-0.848788\pi$
$919$	3.00135	−	9.23720i	0.0990054	−	0.304707i	0.988277	+	0.152673i	$0.0487880\pi$
$920$	88.9878	−	64.6534i	2.93384	−	2.13156i
$921$		0			0
$922$	−12.6530	−	38.9420i	−0.416705	−	1.28249i
$923$	7.81205			0.257137
$924$		0			0
$925$	−30.8169			−1.01325
$926$	−10.4063	−	32.0273i	−0.341972	−	1.05248i
$927$		0			0
$928$	7.57838	−	5.50601i	0.248772	−	0.180744i
$929$	−14.6361	+	45.0454i	−0.480196	+	1.47789i	0.358623	+	0.933482i	$0.383246\pi$
$929$	−14.6361	+	45.0454i	−0.480196	+	1.47789i	−0.838820	+	0.544410i	$0.816754\pi$
$930$		0			0
$931$	−2.59795	+	1.88752i	−0.0851442	+	0.0618609i
$932$	−41.9521	−	30.4800i	−1.37419	−	0.998406i
$933$		0			0
$934$	8.95301			0.292951
$935$	−41.5821	−	11.4832i	−1.35988	−	0.375542i
$936$		0			0
$937$	−8.73057	−	26.8699i	−0.285215	−	0.877802i	−0.986334	−	0.164758i	$-0.947316\pi$
$937$	−8.73057	−	26.8699i	−0.285215	−	0.877802i	0.701119	−	0.713044i	$-0.252684\pi$
$938$	−44.1127	−	32.0497i	−1.44033	−	1.04646i
$939$		0			0
$940$	14.2442	−	43.8391i	0.464594	−	1.42987i
$941$	−17.1866	+	52.8948i	−0.560266	+	1.72432i	0.121349	+	0.992610i	$0.461278\pi$
$941$	−17.1866	+	52.8948i	−0.560266	+	1.72432i	−0.681615	+	0.731711i	$0.738722\pi$
$942$		0			0
$943$	−33.3279	−	24.2141i	−1.08531	−	0.788521i
$944$	0.594580	+	1.82993i	0.0193519	+	0.0595591i
$945$		0			0
$946$	−49.7573	−	62.4147i	−1.61775	−	2.02928i
$947$	44.7602			1.45451			0.727255	−	0.686367i	$-0.240796\pi$
$947$	44.7602			1.45451			0.727255	+	0.686367i	$0.240796\pi$
$948$		0			0
$949$	10.1743	+	7.39207i	0.330272	+	0.239957i
$950$	−36.7211	+	26.6794i	−1.19139	+	0.865595i
$951$		0			0
$952$	−11.9109	+	36.6579i	−0.386034	+	1.18809i
$953$	24.5429	−	17.8315i	0.795023	−	0.577618i	−0.114427	−	0.993432i	$-0.536503\pi$
$953$	24.5429	−	17.8315i	0.795023	−	0.577618i	0.909450	+	0.415814i	$0.136503\pi$
$954$		0			0
$955$	1.94894	+	5.99823i	0.0630663	+	0.194098i
$956$	−25.6815			−0.830598
$957$		0			0
$958$	49.0438			1.58453
$959$	4.70910	+	14.4931i	0.152065	+	0.468007i
$960$		0			0
$961$	−44.4715	+	32.3105i	−1.43457	+	1.04227i
$962$	−2.52574	+	7.77344i	−0.0814332	+	0.250626i
$963$		0			0
$964$	21.7909	−	15.8320i	0.701837	−	0.509914i
$965$	22.1355	+	16.0824i	0.712566	+	0.517709i
$966$		0			0
$967$	49.4090			1.58889			0.794443	−	0.607339i	$-0.207763\pi$
$967$	49.4090			1.58889			0.794443	+	0.607339i	$0.207763\pi$
$968$	−39.1024	+	3.50639i	−1.25680	+	0.112700i
$969$		0			0
$970$	25.8099	+	79.4346i	0.828705	+	2.55049i
$971$	33.4412	+	24.2964i	1.07318	+	0.779710i	0.976481	−	0.215604i	$-0.0691721\pi$
$971$	33.4412	+	24.2964i	1.07318	+	0.779710i	0.0966973	+	0.995314i	$0.469172\pi$
$972$		0			0
$973$	4.63791	−	14.2740i	0.148684	−	0.457604i
$974$	0.0501218	−	0.154259i	0.00160601	−	0.00494278i
$975$		0			0
$976$	−0.598948	−	0.435161i	−0.0191719	−	0.0139292i
$977$	−15.9060	−	48.9535i	−0.508877	−	1.56616i	−0.794154	−	0.607716i	$-0.792086\pi$
$977$	−15.9060	−	48.9535i	−0.508877	−	1.56616i	0.285277	−	0.958445i	$-0.407914\pi$
$978$		0			0
$979$	5.34604	−	2.00541i	0.170860	−	0.0640931i
$980$	−13.6386			−0.435669
$981$		0			0
$982$	65.3927	+	47.5106i	2.08677	+	1.51612i
$983$	−37.1563	+	26.9956i	−1.18510	+	0.861026i	−0.992738	−	0.120297i	$-0.961615\pi$
$983$	−37.1563	+	26.9956i	−1.18510	+	0.861026i	−0.192363	+	0.981324i	$0.561615\pi$
$984$		0			0
$985$	−19.6324	+	60.4223i	−0.625540	+	1.92521i
$986$	−16.9653	+	12.3260i	−0.540287	+	0.392541i
$987$		0			0
$988$	2.37206	+	7.30046i	0.0754654	+	0.232259i
$989$	91.9471			2.92375
$990$		0			0
$991$	22.2929			0.708156			0.354078	−	0.935216i	$-0.384795\pi$
$991$	22.2929			0.708156			0.354078	+	0.935216i	$0.384795\pi$
$992$	−11.3896	−	35.0536i	−0.361620	−	1.11295i
$993$		0			0
$994$	55.2182	−	40.1184i	1.75141	−	1.27248i
$995$	22.0839	−	67.9672i	0.700106	−	2.15470i
$996$		0			0
$997$	−21.4812	+	15.6070i	−0.680315	+	0.494278i	−0.873462	−	0.486892i	$-0.838131\pi$
$997$	−21.4812	+	15.6070i	−0.680315	+	0.494278i	0.193147	+	0.981170i	$0.438131\pi$
$998$	−61.1928	−	44.4592i	−1.93703	−	1.40733i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.a.82.4	✓	16
3.2	odd	2		297.2.f.d.82.1	yes	16
9.2	odd	6		891.2.n.f.676.1		32
9.4	even	3		891.2.n.i.379.1		32
9.5	odd	6		891.2.n.f.379.4		32
9.7	even	3		891.2.n.i.676.4		32
11.3	even	5		3267.2.a.bm.1.7		8
11.8	odd	10		3267.2.a.bf.1.2		8
11.9	even	5	inner	297.2.f.a.163.4	yes	16
33.8	even	10		3267.2.a.bl.1.7		8
33.14	odd	10		3267.2.a.be.1.2		8
33.20	odd	10		297.2.f.d.163.1	yes	16
99.20	odd	30		891.2.n.f.757.4		32
99.31	even	15		891.2.n.i.460.4		32
99.86	odd	30		891.2.n.f.460.1		32
99.97	even	15		891.2.n.i.757.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.82.4	✓	16	1.1	even	1	trivial
297.2.f.a.163.4	yes	16	11.9	even	5	inner
297.2.f.d.82.1	yes	16	3.2	odd	2
297.2.f.d.163.1	yes	16	33.20	odd	10
891.2.n.f.379.4		32	9.5	odd	6
891.2.n.f.460.1		32	99.86	odd	30
891.2.n.f.676.1		32	9.2	odd	6
891.2.n.f.757.4		32	99.20	odd	30
891.2.n.i.379.1		32	9.4	even	3
891.2.n.i.460.4		32	99.31	even	15
891.2.n.i.676.4		32	9.7	even	3
891.2.n.i.757.1		32	99.97	even	15
3267.2.a.be.1.2		8	33.14	odd	10
3267.2.a.bf.1.2		8	11.8	odd	10
3267.2.a.bl.1.7		8	33.8	even	10
3267.2.a.bm.1.7		8	11.3	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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.725972 + 2.23431i) q^{2} +(-2.84709 + 2.06853i) q^{4} +(-1.06108 + 3.26568i) q^{5} +(2.30657 - 1.67582i) q^{7} +(-2.88741 - 2.09782i) q^{8} +O(q^{10})\)	\(q+(0.725972 + 2.23431i) q^{2} +(-2.84709 + 2.06853i) q^{4} +(-1.06108 + 3.26568i) q^{5} +(2.30657 - 1.67582i) q^{7} +(-2.88741 - 2.09782i) q^{8} -8.06687 q^{10} +(-3.10533 + 1.16487i) q^{11} +(0.236903 + 0.729111i) q^{13} +(5.41882 + 3.93700i) q^{14} +(0.416037 - 1.28043i) q^{16} +(1.17053 - 3.60253i) q^{17} +(-2.30182 - 1.67237i) q^{19} +(-3.73416 - 11.4926i) q^{20} +(-4.85707 - 6.09262i) q^{22} +8.97543 q^{23} +(-5.49369 - 3.99140i) q^{25} +(-1.45708 + 1.05863i) q^{26} +(-3.10052 + 9.54242i) q^{28} +(-1.90644 + 1.38511i) q^{29} +(2.86520 + 8.81819i) q^{31} -3.97515 q^{32} +8.89897 q^{34} +(3.02524 + 9.31072i) q^{35} +(3.67146 - 2.66747i) q^{37} +(2.06554 - 6.35708i) q^{38} +(9.91460 - 7.20338i) q^{40} +(-3.71324 - 2.69783i) q^{41} +10.2443 q^{43} +(6.43157 - 9.73995i) q^{44} +(6.51591 + 20.0539i) q^{46} +(3.08604 + 2.24214i) q^{47} +(0.348772 - 1.07341i) q^{49} +(4.92977 - 15.1723i) q^{50} +(-2.18267 - 1.58580i) q^{52} +(1.93120 + 5.94363i) q^{53} +(-0.509080 - 11.3770i) q^{55} -10.1756 q^{56} +(-4.47879 - 3.25403i) q^{58} +(-1.15621 + 0.840035i) q^{59} +(0.169928 - 0.522984i) q^{61} +(-17.6225 + 12.8035i) q^{62} +(-3.71792 - 11.4426i) q^{64} -2.63242 q^{65} -8.14064 q^{67} +(4.11933 + 12.6780i) q^{68} +(-18.6068 + 13.5186i) q^{70} +(3.14891 - 9.69134i) q^{71} +(13.2714 - 9.64225i) q^{73} +(8.62535 + 6.26669i) q^{74} +10.0128 q^{76} +(-5.21055 + 7.89084i) q^{77} +(0.890062 + 2.73933i) q^{79} +(3.74003 + 2.71729i) q^{80} +(3.33208 - 10.2551i) q^{82} +(0.500768 - 1.54120i) q^{83} +(10.5227 + 7.64519i) q^{85} +(7.43709 + 22.8890i) q^{86} +(11.4100 + 3.15098i) q^{88} -1.72157 q^{89} +(1.76829 + 1.28474i) q^{91} +(-25.5538 + 18.5659i) q^{92} +(-2.76926 + 8.52292i) q^{94} +(7.90385 - 5.74248i) q^{95} +(-3.19949 - 9.84701i) q^{97} +2.65153 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7	\( 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7} + 6 q^{10} - 13 q^{11} - 2 q^{13} + 22 q^{14} - 24 q^{16} + 2 q^{17} - 2 q^{19} + 15 q^{22} - 14 q^{23} - 19 q^{25} - 21 q^{26} + 15 q^{28} - q^{29} + 14 q^{31} + 48 q^{32} + 10 q^{34} + 18 q^{35} + 9 q^{37} - 11 q^{38} + 33 q^{40} - 25 q^{41} + 14 q^{43} - 14 q^{44} + 4 q^{46} + 28 q^{47} - 4 q^{49} + 63 q^{50} + 10 q^{52} - q^{53} - 40 q^{55} - 96 q^{56} - 20 q^{58} - 41 q^{59} + 5 q^{62} - 92 q^{64} + 60 q^{65} - 48 q^{67} - 25 q^{68} - 31 q^{70} - 3 q^{71} - 13 q^{73} - 29 q^{74} - 58 q^{76} + 2 q^{77} + 83 q^{80} + 41 q^{82} + 14 q^{83} - 10 q^{85} + 56 q^{86} + 86 q^{88} - 82 q^{89} + 14 q^{91} - 74 q^{92} - 2 q^{94} + 56 q^{95} + 12 q^{97} - 26 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 - q^5 - 2 * q^7 + 6 * q^10 - 13 * q^11 - 2 * q^13 + 22 * q^14 - 24 * q^16 + 2 * q^17 - 2 * q^19 + 15 * q^22 - 14 * q^23 - 19 * q^25 - 21 * q^26 + 15 * q^28 - q^29 + 14 * q^31 + 48 * q^32 + 10 * q^34 + 18 * q^35 + 9 * q^37 - 11 * q^38 + 33 * q^40 - 25 * q^41 + 14 * q^43 - 14 * q^44 + 4 * q^46 + 28 * q^47 - 4 * q^49 + 63 * q^50 + 10 * q^52 - q^53 - 40 * q^55 - 96 * q^56 - 20 * q^58 - 41 * q^59 + 5 * q^62 - 92 * q^64 + 60 * q^65 - 48 * q^67 - 25 * q^68 - 31 * q^70 - 3 * q^71 - 13 * q^73 - 29 * q^74 - 58 * q^76 + 2 * q^77 + 83 * q^80 + 41 * q^82 + 14 * q^83 - 10 * q^85 + 56 * q^86 + 86 * q^88 - 82 * q^89 + 14 * q^91 - 74 * q^92 - 2 * q^94 + 56 * q^95 + 12 * q^97 - 26 * q^98

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