LMFDB - Embedded newform 297.2.f.a.190.2

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			190.2
Root			$-0.175229 - 0.127311i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.a.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984246 + 0.715096i) q^{2} +(-0.160657 + 0.494452i) q^{4} +(-0.240251 - 0.174552i) q^{5} +(1.32806 - 4.08735i) q^{7} +(-0.947351 - 2.91565i) q^{8} +O(q^{10})$	\(q+(-0.984246 + 0.715096i) q^{2} +(-0.160657 + 0.494452i) q^{4} +(-0.240251 - 0.174552i) q^{5} +(1.32806 - 4.08735i) q^{7} +(-0.947351 - 2.91565i) q^{8} +0.361288 q^{10} +(-2.91081 - 1.58971i) q^{11} +(3.06143 - 2.22426i) q^{13} +(1.61571 + 4.97265i) q^{14} +(2.17618 + 1.58109i) q^{16} +(1.09583 + 0.796170i) q^{17} +(1.01673 + 3.12917i) q^{19} +(0.124906 - 0.0907493i) q^{20} +(4.00175 - 0.516838i) q^{22} +4.75523 q^{23} +(-1.51783 - 4.67141i) q^{25} +(-1.42264 + 4.37843i) q^{26} +(1.80763 + 1.31332i) q^{28} +(3.09579 - 9.52785i) q^{29} +(-4.15291 + 3.01727i) q^{31} +2.85886 q^{32} -1.64791 q^{34} +(-1.03252 + 0.750173i) q^{35} +(1.40015 - 4.30921i) q^{37} +(-3.23837 - 2.35281i) q^{38} +(-0.281331 + 0.865849i) q^{40} +(1.87805 + 5.78003i) q^{41} -7.92922 q^{43} +(1.25368 - 1.18386i) q^{44} +(-4.68032 + 3.40045i) q^{46} +(1.47844 + 4.55017i) q^{47} +(-9.27956 - 6.74199i) q^{49} +(4.83443 + 3.51242i) q^{50} +(0.607948 + 1.87107i) q^{52} +(1.16402 - 0.845714i) q^{53} +(0.421835 + 0.890019i) q^{55} -13.1754 q^{56} +(3.76632 + 11.5915i) q^{58} +(1.95315 - 6.01118i) q^{59} +(9.41653 + 6.84151i) q^{61} +(1.92985 - 5.93946i) q^{62} +(-7.16618 + 5.20654i) q^{64} -1.12376 q^{65} -2.68331 q^{67} +(-0.569722 + 0.413927i) q^{68} +(0.479812 - 1.47671i) q^{70} +(-5.17360 - 3.75884i) q^{71} +(0.511265 - 1.57351i) q^{73} +(1.70341 + 5.24256i) q^{74} -1.71057 q^{76} +(-10.3634 + 9.78625i) q^{77} +(-5.52312 + 4.01278i) q^{79} +(-0.246847 - 0.759716i) q^{80} +(-5.98174 - 4.34599i) q^{82} +(-4.08880 - 2.97069i) q^{83} +(-0.124302 - 0.382561i) q^{85} +(7.80430 - 5.67016i) q^{86} +(-1.87749 + 9.99291i) q^{88} -16.3224 q^{89} +(-5.02556 - 15.4671i) q^{91} +(-0.763962 + 2.35123i) q^{92} +(-4.70896 - 3.42126i) q^{94} +(0.301934 - 0.929258i) q^{95} +(-3.15857 + 2.29484i) q^{97} +13.9545 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.984246	+	0.715096i	−0.695967	+	0.505650i	−0.878616	−	0.477529i	$-0.841533\pi$
$2$	−0.984246	+	0.715096i	−0.695967	+	0.505650i	0.182649	+	0.983178i	$0.441533\pi$
$3$		0			0
$3$		0			0
$4$	−0.160657	+	0.494452i	−0.0803286	+	0.247226i
$5$	−0.240251	−	0.174552i	−0.107443	−	0.0780622i	0.532766	−	0.846262i	$-0.321153\pi$
$5$	−0.240251	−	0.174552i	−0.107443	−	0.0780622i	−0.640210	+	0.768200i	$0.721153\pi$
$6$		0			0
$7$	1.32806	−	4.08735i	0.501960	−	1.54487i	−0.303863	−	0.952716i	$-0.598277\pi$
$7$	1.32806	−	4.08735i	0.501960	−	1.54487i	0.805823	−	0.592157i	$-0.201723\pi$
$8$	−0.947351	−	2.91565i	−0.334939	−	1.03084i
$9$		0			0
$10$	0.361288			0.114249
$11$	−2.91081	−	1.58971i	−0.877642	−	0.479317i
$11$	−2.91081	−	1.58971i	−0.877642	−	0.479317i
$12$		0			0
$13$	3.06143	−	2.22426i	0.849087	−	0.616898i	−0.0758070	−	0.997123i	$-0.524153\pi$
$13$	3.06143	−	2.22426i	0.849087	−	0.616898i	0.924894	+	0.380225i	$0.124153\pi$
$14$	1.61571	+	4.97265i	0.431817	+	1.32900i
$15$		0			0
$16$	2.17618	+	1.58109i	0.544046	+	0.395273i
$17$	1.09583	+	0.796170i	0.265779	+	0.193100i	0.712691	−	0.701478i	$-0.247476\pi$
$17$	1.09583	+	0.796170i	0.265779	+	0.193100i	−0.446912	+	0.894578i	$0.647476\pi$
$18$		0			0
$19$	1.01673	+	3.12917i	0.233254	+	0.717881i	0.997348	+	0.0727768i	$0.0231861\pi$
$19$	1.01673	+	3.12917i	0.233254	+	0.717881i	−0.764095	+	0.645104i	$0.776814\pi$
$20$	0.124906	−	0.0907493i	0.0279298	−	0.0202922i
$21$		0			0
$22$	4.00175	−	0.516838i	0.853176	−	0.110190i
$23$	4.75523			0.991534			0.495767	−	0.868456i	$-0.334887\pi$
$23$	4.75523			0.991534			0.495767	+	0.868456i	$0.334887\pi$
$24$		0			0
$25$	−1.51783	−	4.67141i	−0.303567	−	0.934282i
$26$	−1.42264	+	4.37843i	−0.279002	+	0.858681i
$27$		0			0
$28$	1.80763	+	1.31332i	0.341611	+	0.248195i
$29$	3.09579	−	9.52785i	0.574873	−	1.76928i	−0.0617370	−	0.998092i	$-0.519664\pi$
$29$	3.09579	−	9.52785i	0.574873	−	1.76928i	0.636610	−	0.771186i	$-0.280336\pi$
$30$		0			0
$31$	−4.15291	+	3.01727i	−0.745885	+	0.541917i	−0.894549	−	0.446971i	$-0.852503\pi$
$31$	−4.15291	+	3.01727i	−0.745885	+	0.541917i	0.148664	+	0.988888i	$0.452503\pi$
$32$	2.85886			0.505379
$33$		0			0
$34$	−1.64791			−0.282614
$35$	−1.03252	+	0.750173i	−0.174528	+	0.126802i
$36$		0			0
$37$	1.40015	−	4.30921i	0.230183	−	0.708429i	−0.767541	−	0.640999i	$-0.778520\pi$
$37$	1.40015	−	4.30921i	0.230183	−	0.708429i	0.997724	−	0.0674299i	$-0.0214799\pi$
$38$	−3.23837	−	2.35281i	−0.525333	−	0.381677i
$39$		0			0
$40$	−0.281331	+	0.865849i	−0.0444824	+	0.136903i
$41$	1.87805	+	5.78003i	0.293301	+	0.902689i	0.983787	+	0.179342i	$0.0573970\pi$
$41$	1.87805	+	5.78003i	0.293301	+	0.902689i	−0.690485	+	0.723346i	$0.742603\pi$
$42$		0			0
$43$	−7.92922			−1.20919			−0.604597	−	0.796531i	$-0.706666\pi$
$43$	−7.92922			−1.20919			−0.604597	+	0.796531i	$0.706666\pi$
$44$	1.25368	−	1.18386i	0.188999	−	0.178473i
$45$		0			0
$46$	−4.68032	+	3.40045i	−0.690075	+	0.501369i
$47$	1.47844	+	4.55017i	0.215652	+	0.663710i	0.999107	+	0.0422605i	$0.0134559\pi$
$47$	1.47844	+	4.55017i	0.215652	+	0.663710i	−0.783454	+	0.621450i	$0.786544\pi$
$48$		0			0
$49$	−9.27956	−	6.74199i	−1.32565	−	0.963142i
$50$	4.83443	+	3.51242i	0.683692	+	0.496731i
$51$		0			0
$52$	0.607948	+	1.87107i	0.0843072	+	0.259471i
$53$	1.16402	−	0.845714i	0.159891	−	0.116168i	−0.504963	−	0.863141i	$-0.668494\pi$
$53$	1.16402	−	0.845714i	0.159891	−	0.116168i	0.664854	+	0.746973i	$0.268494\pi$
$54$		0			0
$55$	0.421835	+	0.890019i	0.0568803	+	0.120010i
$56$	−13.1754			−1.76064
$57$		0			0
$58$	3.76632	+	11.5915i	0.494542	+	1.52204i
$59$	1.95315	−	6.01118i	0.254278	−	0.782588i	−0.739693	−	0.672945i	$-0.765029\pi$
$59$	1.95315	−	6.01118i	0.254278	−	0.782588i	0.993971	−	0.109643i	$-0.0349709\pi$
$60$		0			0
$61$	9.41653	+	6.84151i	1.20566	+	0.875966i	0.994830	−	0.101556i	$-0.0323821\pi$
$61$	9.41653	+	6.84151i	1.20566	+	0.875966i	0.210834	+	0.977522i	$0.432382\pi$
$62$	1.92985	−	5.93946i	0.245091	−	0.754313i
$63$		0			0
$64$	−7.16618	+	5.20654i	−0.895773	+	0.650817i
$65$	−1.12376			−0.139385
$66$		0			0
$67$	−2.68331			−0.327819			−0.163909	−	0.986475i	$-0.552410\pi$
$67$	−2.68331			−0.327819			−0.163909	+	0.986475i	$0.552410\pi$
$68$	−0.569722	+	0.413927i	−0.0690889	+	0.0501960i
$69$		0			0
$70$	0.479812	−	1.47671i	0.0573485	−	0.176500i
$71$	−5.17360	−	3.75884i	−0.613994	−	0.446093i	0.236825	−	0.971552i	$-0.423893\pi$
$71$	−5.17360	−	3.75884i	−0.613994	−	0.446093i	−0.850818	+	0.525460i	$0.823893\pi$
$72$		0			0
$73$	0.511265	−	1.57351i	0.0598390	−	0.184165i	−0.916669	−	0.399648i	$-0.869132\pi$
$73$	0.511265	−	1.57351i	0.0598390	−	0.184165i	0.976508	+	0.215482i	$0.0691324\pi$
$74$	1.70341	+	5.24256i	0.198017	+	0.609435i
$75$		0			0
$76$	−1.71057			−0.196216
$77$	−10.3634	+	9.78625i	−1.18102	+	1.11525i
$78$		0			0
$79$	−5.52312	+	4.01278i	−0.621400	+	0.451473i	−0.853410	−	0.521240i	$-0.825470\pi$
$79$	−5.52312	+	4.01278i	−0.621400	+	0.451473i	0.232010	+	0.972713i	$0.425470\pi$
$80$	−0.246847	−	0.759716i	−0.0275983	−	0.0849389i
$81$		0			0
$82$	−5.98174	−	4.34599i	−0.660572	−	0.479934i
$83$	−4.08880	−	2.97069i	−0.448805	−	0.326076i	0.340319	−	0.940310i	$-0.389465\pi$
$83$	−4.08880	−	2.97069i	−0.448805	−	0.326076i	−0.789124	+	0.614234i	$0.789465\pi$
$84$		0			0
$85$	−0.124302	−	0.382561i	−0.0134824	−	0.0414946i
$86$	7.80430	−	5.67016i	0.841559	−	0.611429i
$87$		0			0
$88$	−1.87749	+	9.99291i	−0.200141	+	1.06525i
$89$	−16.3224			−1.73017			−0.865086	−	0.501623i	$-0.832736\pi$
$89$	−16.3224			−1.73017			−0.865086	+	0.501623i	$0.832736\pi$
$90$		0			0
$91$	−5.02556	−	15.4671i	−0.526821	−	1.62139i
$92$	−0.763962	+	2.35123i	−0.0796485	+	0.245133i
$93$		0			0
$94$	−4.70896	−	3.42126i	−0.485692	−	0.352876i
$95$	0.301934	−	0.929258i	0.0309778	−	0.0953399i
$96$		0			0
$97$	−3.15857	+	2.29484i	−0.320705	+	0.233006i	−0.736476	−	0.676464i	$-0.763512\pi$
$97$	−3.15857	+	2.29484i	−0.320705	+	0.233006i	0.415771	+	0.909469i	$0.363512\pi$
$98$	13.9545			1.40962
$99$		0			0
$100$	2.55364			0.255364
$101$	8.74596	−	6.35431i	0.870256	−	0.632278i	−0.0603998	−	0.998174i	$-0.519238\pi$
$101$	8.74596	−	6.35431i	0.870256	−	0.632278i	0.930656	+	0.365896i	$0.119238\pi$
$102$		0			0
$103$	1.35656	−	4.17506i	0.133666	−	0.411381i	−0.861714	−	0.507394i	$-0.830609\pi$
$103$	1.35656	−	4.17506i	0.133666	−	0.411381i	0.995380	+	0.0960129i	$0.0306090\pi$
$104$	−9.38540	−	6.81889i	−0.920314	−	0.668647i
$105$		0			0
$106$	−0.540920	+	1.66478i	−0.0525388	+	0.161698i
$107$	4.31866	+	13.2915i	0.417500	+	1.28493i	0.909995	+	0.414619i	$0.136085\pi$
$107$	4.31866	+	13.2915i	0.417500	+	1.28493i	−0.492495	+	0.870315i	$0.663915\pi$
$108$		0			0
$109$	10.9437			1.04822			0.524109	−	0.851651i	$-0.324398\pi$
$109$	10.9437			1.04822			0.524109	+	0.851651i	$0.324398\pi$
$110$	−1.05164	−	0.574344i	−0.100270	−	0.0547616i
$111$		0			0
$112$	9.35257	−	6.79504i	0.883735	−	0.642071i
$113$	1.61382	+	4.96682i	0.151815	+	0.467239i	0.997824	−	0.0659294i	$-0.0210012\pi$
$113$	1.61382	+	4.96682i	0.151815	+	0.467239i	−0.846009	+	0.533168i	$0.821001\pi$
$114$		0			0
$115$	−1.14245	−	0.830037i	−0.106534	−	0.0774013i
$116$	4.21370	+	3.06144i	0.391233	+	0.284247i
$117$		0			0
$118$	2.37619	+	7.31316i	0.218746	+	0.673231i
$119$	4.70956	−	3.42170i	0.431725	−	0.313666i
$120$		0			0
$121$	5.94561	+	9.25471i	0.540510	+	0.841337i
$122$	−14.1605			−1.28203
$123$		0			0
$124$	−0.824698	−	2.53816i	−0.0740601	−	0.227933i
$125$	−0.909583	+	2.79941i	−0.0813556	+	0.250387i
$126$		0			0
$127$	1.21650	+	0.883841i	0.107947	+	0.0784282i	0.640449	−	0.768000i	$-0.278748\pi$
$127$	1.21650	+	0.883841i	0.107947	+	0.0784282i	−0.532502	+	0.846429i	$0.678748\pi$
$128$	1.56324	−	4.81116i	0.138172	−	0.425251i
$129$		0			0
$130$	1.10606	−	0.803597i	0.0970075	−	0.0704801i
$131$	19.3527			1.69085			0.845425	−	0.534094i	$-0.179347\pi$
$131$	19.3527			1.69085			0.845425	+	0.534094i	$0.179347\pi$
$132$		0			0
$133$	14.1403			1.22612
$134$	2.64104	−	1.91883i	0.228151	−	0.165761i
$135$		0			0
$136$	1.28321	−	3.94932i	0.110035	−	0.338652i
$137$	16.2477	+	11.8046i	1.38813	+	1.00854i	0.996067	+	0.0886000i	$0.0282393\pi$
$137$	16.2477	+	11.8046i	1.38813	+	1.00854i	0.392065	+	0.919937i	$0.371761\pi$
$138$		0			0
$139$	3.80522	−	11.7113i	0.322755	−	0.993337i	−0.649689	−	0.760200i	$-0.725101\pi$
$139$	3.80522	−	11.7113i	0.322755	−	0.993337i	0.972444	−	0.233137i	$-0.0748990\pi$
$140$	−0.205042	−	0.631054i	−0.0173292	−	0.0533338i
$141$		0			0
$142$	7.78003			0.652886
$143$	−12.4472	+	1.60759i	−1.04088	+	0.134433i
$144$		0			0
$145$	−2.40688	+	1.74870i	−0.199880	+	0.145221i
$146$	0.622002	+	1.91432i	0.0514772	+	0.158431i
$147$		0			0
$148$	1.90575	+	1.38461i	0.156652	+	0.113814i
$149$	−10.2763	−	7.46614i	−0.841863	−	0.611650i	0.0810271	−	0.996712i	$-0.474180\pi$
$149$	−10.2763	−	7.46614i	−0.841863	−	0.611650i	−0.922891	+	0.385062i	$0.874180\pi$
$150$		0			0
$151$	−2.13594	−	6.57375i	−0.173820	−	0.534964i	0.825757	−	0.564026i	$-0.190748\pi$
$151$	−2.13594	−	6.57375i	−0.173820	−	0.534964i	−0.999578	+	0.0290617i	$0.990748\pi$
$152$	8.16036	−	5.92885i	0.661893	−	0.480893i
$153$		0			0
$154$	3.20207	−	17.0429i	0.258030	−	1.37336i
$155$	1.52441			0.122444
$156$		0			0
$157$	2.03115	+	6.25123i	0.162103	+	0.498902i	0.998811	−	0.0487470i	$-0.0155228\pi$
$157$	2.03115	+	6.25123i	0.162103	+	0.498902i	−0.836708	+	0.547649i	$0.815523\pi$
$158$	2.56658	−	7.89913i	0.204186	−	0.628421i
$159$		0			0
$160$	−0.686842	−	0.499020i	−0.0542996	−	0.0394510i
$161$	6.31523	−	19.4363i	0.497710	−	1.53179i
$162$		0			0
$163$	−2.60590	+	1.89330i	−0.204110	+	0.148294i	−0.685145	−	0.728407i	$-0.740261\pi$
$163$	−2.60590	+	1.89330i	−0.204110	+	0.148294i	0.481035	+	0.876701i	$0.340261\pi$
$164$	−3.15967			−0.246729
$165$		0			0
$166$	6.14872			0.477233
$167$	−8.45582	+	6.14351i	−0.654331	+	0.475399i	−0.864744	−	0.502213i	$-0.832519\pi$
$167$	−8.45582	+	6.14351i	−0.654331	+	0.475399i	0.210413	+	0.977613i	$0.432519\pi$
$168$		0			0
$169$	0.407796	−	1.25507i	0.0313690	−	0.0965437i
$170$	0.395911	+	0.287647i	0.0303650	+	0.0220615i
$171$		0			0
$172$	1.27389	−	3.92062i	0.0971329	−	0.298944i
$173$	4.09941	+	12.6167i	0.311672	+	0.959229i	0.977103	+	0.212769i	$0.0682481\pi$
$173$	4.09941	+	12.6167i	0.311672	+	0.959229i	−0.665430	+	0.746460i	$0.731752\pi$
$174$		0			0
$175$	−21.1095			−1.59572
$176$	−3.82097	−	8.06176i	−0.288017	−	0.607678i
$177$		0			0
$178$	16.0653	−	11.6721i	1.20414	−	0.874861i
$179$	6.05961	+	18.6496i	0.452917	+	1.39393i	0.873564	+	0.486710i	$0.161803\pi$
$179$	6.05961	+	18.6496i	0.452917	+	1.39393i	−0.420647	+	0.907224i	$0.638197\pi$
$180$		0			0
$181$	20.7377	+	15.0668i	1.54142	+	1.11991i	0.949435	+	0.313962i	$0.101657\pi$
$181$	20.7377	+	15.0668i	1.54142	+	1.11991i	0.591988	+	0.805947i	$0.298343\pi$
$182$	16.0068	+	11.6296i	1.18650	+	0.862046i
$183$		0			0
$184$	−4.50487	−	13.8646i	−0.332104	−	1.02211i
$185$	−1.08857	+	0.790892i	−0.0800332	+	0.0581475i
$186$		0			0
$187$	−1.92408	−	4.05956i	−0.140703	−	0.296865i
$188$	−2.48736			−0.181409
$189$		0			0
$190$	0.367332	+	1.13053i	0.0266490	+	0.0820173i
$191$	−4.75946	+	14.6481i	−0.344383	+	1.05990i	0.617531	+	0.786547i	$0.288133\pi$
$191$	−4.75946	+	14.6481i	−0.344383	+	1.05990i	−0.961914	+	0.273354i	$0.911867\pi$
$192$		0			0
$193$	11.3997	+	8.28236i	0.820568	+	0.596178i	0.916875	−	0.399174i	$-0.130703\pi$
$193$	11.3997	+	8.28236i	0.820568	+	0.596178i	−0.0963071	+	0.995352i	$0.530703\pi$
$194$	1.46778	−	4.51737i	0.105381	−	0.324328i
$195$		0			0
$196$	4.82442	−	3.50515i	0.344601	−	0.250368i
$197$	−5.14056			−0.366250			−0.183125	−	0.983090i	$-0.558621\pi$
$197$	−5.14056			−0.366250			−0.183125	+	0.983090i	$0.558621\pi$
$198$		0			0
$199$	−15.9561			−1.13109			−0.565547	−	0.824716i	$-0.691335\pi$
$199$	−15.9561			−1.13109			−0.565547	+	0.824716i	$0.691335\pi$
$200$	−12.1823	+	8.85093i	−0.861416	+	0.625856i
$201$		0			0
$202$	−4.06423	+	12.5084i	−0.285958	+	0.880089i
$203$	−34.8323	−	25.3071i	−2.44475	−	1.77621i
$204$		0			0
$205$	0.557716	−	1.71647i	0.0389526	−	0.119884i
$206$	1.65038	+	5.07935i	0.114988	+	0.353895i
$207$		0			0
$208$	10.1790			0.705785
$209$	2.01499	−	10.7247i	0.139379	−	0.741845i
$210$		0			0
$211$	−7.70960	+	5.60135i	−0.530751	+	0.385613i	−0.820639	−	0.571448i	$-0.806382\pi$
$211$	−7.70960	+	5.60135i	−0.530751	+	0.385613i	0.289888	+	0.957061i	$0.406382\pi$
$212$	0.231156	+	0.711424i	0.0158758	+	0.0488608i
$213$		0			0
$214$	−13.7553	−	9.99381i	−0.940293	−	0.683163i
$215$	1.90500	+	1.38406i	0.129920	+	0.0943924i
$216$		0			0
$217$	6.81731	+	20.9815i	0.462789	+	1.42432i
$218$	−10.7713	+	7.82582i	−0.729525	+	0.530031i
$219$		0			0
$220$	−0.507842	+	0.0655894i	−0.0342387	+	0.00442204i
$221$	5.12571			0.344792
$222$		0			0
$223$	4.75820	+	14.6442i	0.318633	+	0.980651i	0.974233	+	0.225543i	$0.0724155\pi$
$223$	4.75820	+	14.6442i	0.318633	+	0.980651i	−0.655601	+	0.755108i	$0.727584\pi$
$224$	3.79673	−	11.6851i	0.253680	−	0.780746i
$225$		0			0
$226$	−5.14015	−	3.73453i	−0.341917	−	0.248418i
$227$	6.32351	−	19.4618i	0.419706	−	1.29172i	−0.488267	−	0.872694i	$-0.662371\pi$
$227$	6.32351	−	19.4618i	0.419706	−	1.29172i	0.907973	−	0.419028i	$-0.137629\pi$
$228$		0			0
$229$	23.6409	−	17.1762i	1.56224	−	1.13503i	0.628093	−	0.778139i	$-0.283836\pi$
$229$	23.6409	−	17.1762i	1.56224	−	1.13503i	0.934145	−	0.356893i	$-0.116164\pi$
$230$	1.71801			0.113282
$231$		0			0
$232$	−30.7127			−2.01639
$233$	−0.592266	+	0.430306i	−0.0388006	+	0.0281903i	−0.607017	−	0.794689i	$-0.707634\pi$
$233$	−0.592266	+	0.430306i	−0.0388006	+	0.0281903i	0.568216	+	0.822879i	$0.307634\pi$
$234$		0			0
$235$	0.439046	−	1.35125i	0.0286402	−	0.0881456i
$236$	2.65845	+	1.93148i	0.173050	+	0.125728i
$237$		0			0
$238$	−2.18852	+	6.73558i	−0.141861	+	0.436603i
$239$	−7.15672	−	22.0261i	−0.462930	−	1.42475i	−0.861567	−	0.507643i	$-0.830517\pi$
$239$	−7.15672	−	22.0261i	−0.462930	−	1.42475i	0.398637	−	0.917109i	$-0.369483\pi$
$240$		0			0
$241$	−2.60377			−0.167724			−0.0838619	−	0.996477i	$-0.526725\pi$
$241$	−2.60377			−0.167724			−0.0838619	+	0.996477i	$0.526725\pi$
$242$	−12.4700	−	4.85722i	−0.801599	−	0.312234i
$243$		0			0
$244$	−4.89563	+	3.55688i	−0.313411	+	0.227706i
$245$	1.05259	+	3.23954i	0.0672475	+	0.206967i
$246$		0			0
$247$	10.0727	+	7.31826i	0.640912	+	0.465650i
$248$	12.7316	+	9.25002i	0.808454	+	0.587377i
$249$		0			0
$250$	−1.10659	−	3.40575i	−0.0699872	−	0.215398i
$251$	−16.3210	+	11.8579i	−1.03017	+	0.748464i	−0.968343	−	0.249622i	$-0.919694\pi$
$251$	−16.3210	+	11.8579i	−1.03017	+	0.748464i	−0.0618296	+	0.998087i	$0.519694\pi$
$252$		0			0
$253$	−13.8416	−	7.55946i	−0.870212	−	0.475259i
$254$	−1.82937			−0.114785
$255$		0			0
$256$	−3.57265	−	10.9955i	−0.223290	−	0.687217i
$257$	−2.67203	+	8.22366i	−0.166677	+	0.512978i	−0.999156	−	0.0410782i	$-0.986921\pi$
$257$	−2.67203	+	8.22366i	−0.166677	+	0.512978i	0.832479	+	0.554056i	$0.186921\pi$
$258$		0			0
$259$	−15.7538	−	11.4458i	−0.978891	−	0.711206i
$260$	0.180540	−	0.555645i	0.0111966	−	0.0344596i
$261$		0			0
$262$	−19.0478	+	13.8390i	−1.17678	+	0.854977i
$263$	22.4183			1.38237			0.691185	−	0.722678i	$-0.257089\pi$
$263$	22.4183			1.38237			0.691185	+	0.722678i	$0.257089\pi$
$264$		0			0
$265$	−0.427279			−0.0262476
$266$	−13.9175	+	10.1117i	−0.853338	+	0.619986i
$267$		0			0
$268$	0.431094	−	1.32677i	0.0263332	−	0.0810453i
$269$	3.12219	+	2.26840i	0.190363	+	0.138307i	0.678885	−	0.734245i	$-0.262464\pi$
$269$	3.12219	+	2.26840i	0.190363	+	0.138307i	−0.488522	+	0.872552i	$0.662464\pi$
$270$		0			0
$271$	−9.62864	+	29.6339i	−0.584898	+	1.80013i	0.0147800	+	0.999891i	$0.495295\pi$
$271$	−9.62864	+	29.6339i	−0.584898	+	1.80013i	−0.599678	+	0.800241i	$0.704705\pi$
$272$	1.12592	+	3.46523i	0.0682690	+	0.210110i
$273$		0			0
$274$	−24.4332			−1.47606
$275$	−3.00809	+	16.0105i	−0.181395	+	0.965470i
$276$		0			0
$277$	−8.41473	+	6.11366i	−0.505592	+	0.367334i	−0.811149	−	0.584840i	$-0.801157\pi$
$277$	−8.41473	+	6.11366i	−0.505592	+	0.367334i	0.305557	+	0.952174i	$0.401157\pi$
$278$	4.62941	+	14.2479i	0.277654	+	0.854530i
$279$		0			0
$280$	3.16540	+	2.29980i	0.189169	+	0.137439i
$281$	−6.92393	−	5.03053i	−0.413047	−	0.300096i	0.361787	−	0.932261i	$-0.382167\pi$
$281$	−6.92393	−	5.03053i	−0.413047	−	0.300096i	−0.774834	+	0.632165i	$0.782167\pi$
$282$		0			0
$283$	−1.12921	−	3.47536i	−0.0671247	−	0.206588i	0.911868	−	0.410483i	$-0.134640\pi$
$283$	−1.12921	−	3.47536i	−0.0671247	−	0.206588i	−0.978993	+	0.203895i	$0.934640\pi$
$284$	2.68974	−	1.95421i	0.159607	−	0.115961i
$285$		0			0
$286$	11.1015	−	10.4832i	0.656445	−	0.619884i
$287$	26.1192			1.54176
$288$		0			0
$289$	−4.68632	−	14.4230i	−0.275666	−	0.848413i
$290$	1.11847	−	3.44230i	0.0656788	−	0.202139i
$291$		0			0
$292$	0.695887	+	0.505591i	0.0407237	+	0.0295875i
$293$	1.99718	−	6.14670i	0.116677	−	0.359094i	−0.875616	−	0.483007i	$-0.839544\pi$
$293$	1.99718	−	6.14670i	0.116677	−	0.359094i	0.992293	+	0.123913i	$0.0395444\pi$
$294$		0			0
$295$	−1.51851	+	1.10326i	−0.0884111	+	0.0642344i
$296$	−13.8906			−0.807373
$297$		0			0
$298$	15.4534			0.895189
$299$	14.5578	−	10.5769i	0.841899	−	0.611675i
$300$		0			0
$301$	−10.5305	+	32.4095i	−0.606967	+	1.86805i
$302$	6.80315	+	4.94278i	0.391477	+	0.284425i
$303$		0			0
$304$	−2.73491	+	8.41719i	−0.156858	+	0.482759i
$305$	−1.06813	−	3.28736i	−0.0611608	−	0.188234i
$306$		0			0
$307$	24.8253			1.41686			0.708429	−	0.705782i	$-0.249404\pi$
$307$	24.8253			1.41686			0.708429	+	0.705782i	$0.249404\pi$
$308$	−3.17387	−	6.69646i	−0.180848	−	0.381566i
$309$		0			0
$310$	−1.50040	+	1.09010i	−0.0852167	+	0.0619136i
$311$	−2.91130	−	8.96006i	−0.165085	−	0.508078i	0.833958	−	0.551828i	$-0.186070\pi$
$311$	−2.91130	−	8.96006i	−0.165085	−	0.508078i	−0.999043	+	0.0437498i	$0.986070\pi$
$312$		0			0
$313$	15.0013	+	10.8991i	0.847922	+	0.616051i	0.924572	−	0.381007i	$-0.124423\pi$
$313$	15.0013	+	10.8991i	0.847922	+	0.616051i	−0.0766505	+	0.997058i	$0.524423\pi$
$314$	−6.46938	−	4.70028i	−0.365088	−	0.265252i
$315$		0			0
$316$	−1.09680	−	3.37560i	−0.0616998	−	0.189892i
$317$	4.52524	−	3.28778i	0.254163	−	0.184660i	−0.453407	−	0.891304i	$-0.649792\pi$
$317$	4.52524	−	3.28778i	0.254163	−	0.184660i	0.707570	+	0.706644i	$0.249792\pi$
$318$		0			0
$319$	−24.1578	+	22.8123i	−1.35258	+	1.27725i
$320$	2.63050			0.147049
$321$		0			0
$322$	7.68308	+	23.6461i	0.428161	+	1.31774i
$323$	−1.37719	+	4.23854i	−0.0766287	+	0.235839i
$324$		0			0
$325$	−15.0372	−	10.9251i	−0.834111	−	0.606017i
$326$	1.21096	−	3.72694i	0.0670686	−	0.206416i
$327$		0			0
$328$	15.0734	−	10.9514i	0.832287	−	0.604692i
$329$	20.5616			1.13360
$330$		0			0
$331$	19.4869			1.07110			0.535549	−	0.844504i	$-0.320105\pi$
$331$	19.4869			1.07110			0.535549	+	0.844504i	$0.320105\pi$
$332$	2.12576	−	1.54445i	0.116666	−	0.0847629i
$333$		0			0
$334$	3.92940	−	12.0934i	0.215007	−	0.661724i
$335$	0.644668	+	0.468379i	0.0352220	+	0.0255903i
$336$		0			0
$337$	3.84865	−	11.8449i	0.209649	−	0.645234i	−0.789841	−	0.613312i	$-0.789837\pi$
$337$	3.84865	−	11.8449i	0.209649	−	0.645234i	0.999490	−	0.0319226i	$-0.0101630\pi$
$338$	0.496123	+	1.52691i	0.0269855	+	0.0830529i
$339$		0			0
$340$	0.209128			0.0113416
$341$	16.8849	−	2.18074i	0.914370	−	0.118094i
$342$		0			0
$343$	−15.5424	+	11.2922i	−0.839208	+	0.609720i
$344$	7.51176	+	23.1188i	0.405007	+	1.24648i
$345$		0			0
$346$	−13.0570	−	9.48645i	−0.701947	−	0.509994i
$347$	11.8437	+	8.60492i	0.635801	+	0.461937i	0.858405	−	0.512972i	$-0.171456\pi$
$347$	11.8437	+	8.60492i	0.635801	+	0.461937i	−0.222604	+	0.974909i	$0.571456\pi$
$348$		0			0
$349$	−6.17251	−	18.9970i	−0.330407	−	1.01689i	−0.968941	−	0.247294i	$-0.920459\pi$
$349$	−6.17251	−	18.9970i	−0.330407	−	1.01689i	0.638534	−	0.769594i	$-0.279541\pi$
$350$	20.7769	−	15.0953i	1.11057	−	0.806878i
$351$		0			0
$352$	−8.32158	−	4.54476i	−0.443542	−	0.242237i
$353$	−28.5578			−1.51998			−0.759988	−	0.649937i	$-0.774795\pi$
$353$	−28.5578			−1.51998			−0.759988	+	0.649937i	$0.774795\pi$
$354$		0			0
$355$	0.586847	+	1.80613i	0.0311466	+	0.0958594i
$356$	2.62231	−	8.07065i	0.138982	−	0.427743i
$357$		0			0
$358$	−19.3004	−	14.0226i	−1.02006	−	0.741115i
$359$	−3.82507	+	11.7723i	−0.201879	+	0.621321i	0.797948	+	0.602727i	$0.205919\pi$
$359$	−3.82507	+	11.7723i	−0.201879	+	0.621321i	−0.999827	+	0.0185942i	$0.994081\pi$
$360$		0			0
$361$	6.61335	−	4.80488i	0.348071	−	0.252888i
$362$	−31.1853			−1.63906
$363$		0			0
$364$	8.45511			0.443168
$365$	−0.397492	+	0.288795i	−0.0208057	+	0.0151162i
$366$		0			0
$367$	−7.54711	+	23.2276i	−0.393956	+	1.21247i	0.535816	+	0.844335i	$0.320004\pi$
$367$	−7.54711	+	23.2276i	−0.393956	+	1.21247i	−0.929772	+	0.368136i	$0.879996\pi$
$368$	10.3483	+	7.51845i	0.539440	+	0.391926i
$369$		0			0
$370$	0.505856	−	1.55686i	0.0262982	−	0.0809375i
$371$	−1.91083	−	5.88093i	−0.0992054	−	0.305323i
$372$		0			0
$373$	3.13377			0.162260			0.0811302	−	0.996704i	$-0.474147\pi$
$373$	3.13377			0.162260			0.0811302	+	0.996704i	$0.474147\pi$
$374$	4.79675	+	2.61971i	0.248034	+	0.135462i
$375$		0			0
$376$	11.8661	−	8.62121i	0.611947	−	0.444605i
$377$	−11.7149	−	36.0547i	−0.603346	−	1.85691i
$378$		0			0
$379$	−13.5173	−	9.82092i	−0.694339	−	0.504467i	0.183745	−	0.982974i	$-0.441178\pi$
$379$	−13.5173	−	9.82092i	−0.694339	−	0.504467i	−0.878084	+	0.478507i	$0.841178\pi$
$380$	0.410966	+	0.298584i	0.0210821	+	0.0153170i
$381$		0			0
$382$	−5.79034	−	17.8208i	−0.296259	−	0.911792i
$383$	5.54475	−	4.02850i	0.283324	−	0.205847i	−0.437042	−	0.899441i	$-0.643974\pi$
$383$	5.54475	−	4.02850i	0.283324	−	0.205847i	0.720366	+	0.693594i	$0.243974\pi$
$384$		0			0
$385$	4.19804	−	0.542190i	0.213952	−	0.0276326i
$386$	−17.1428			−0.872545
$387$		0			0
$388$	−0.627240	−	1.93044i	−0.0318433	−	0.0980035i
$389$	−7.37416	+	22.6953i	−0.373885	+	1.15070i	0.570343	+	0.821407i	$0.306810\pi$
$389$	−7.37416	+	22.6953i	−0.373885	+	1.15070i	−0.944228	+	0.329293i	$0.893190\pi$
$390$		0			0
$391$	5.21095	+	3.78597i	0.263529	+	0.191465i
$392$	−10.8663	+	33.4430i	−0.548830	+	1.68913i
$393$		0			0
$394$	5.05957	−	3.67600i	0.254898	−	0.185194i
$395$	2.02738			0.102008
$396$		0			0
$397$	−2.49033			−0.124986			−0.0624931	−	0.998045i	$-0.519905\pi$
$397$	−2.49033			−0.124986			−0.0624931	+	0.998045i	$0.519905\pi$
$398$	15.7047	−	11.4101i	0.787204	−	0.571937i
$399$		0			0
$400$	4.08284	−	12.5657i	0.204142	−	0.628284i
$401$	17.0669	+	12.3998i	0.852279	+	0.619217i	0.925773	−	0.378079i	$-0.123415\pi$
$401$	17.0669	+	12.3998i	0.852279	+	0.619217i	−0.0734947	+	0.997296i	$0.523415\pi$
$402$		0			0
$403$	−6.00266	+	18.4743i	−0.299014	+	0.920270i
$404$	1.73680	+	5.34532i	0.0864091	+	0.265940i
$405$		0			0
$406$	52.3806			2.59960
$407$	−10.9260	+	10.3174i	−0.541580	+	0.511417i
$408$		0			0
$409$	12.3168	−	8.94869i	0.609027	−	0.442484i	−0.240044	−	0.970762i	$-0.577162\pi$
$409$	12.3168	−	8.94869i	0.609027	−	0.442484i	0.849072	+	0.528278i	$0.177162\pi$
$410$	0.678514	+	2.08825i	0.0335094	+	0.103131i
$411$		0			0
$412$	1.84642	+	1.34151i	0.0909668	+	0.0660913i
$413$	−21.9759	−	15.9664i	−1.08136	−	0.785656i
$414$		0			0
$415$	0.463797	+	1.42742i	0.0227669	+	0.0700693i
$416$	8.75218	−	6.35883i	0.429111	−	0.311767i
$417$		0			0
$418$	5.68597	+	11.9967i	0.278110	+	0.586777i
$419$	2.33114			0.113884			0.0569419	−	0.998377i	$-0.481865\pi$
$419$	2.33114			0.113884			0.0569419	+	0.998377i	$0.481865\pi$
$420$		0			0
$421$	−0.585339	−	1.80149i	−0.0285277	−	0.0877991i	0.935779	−	0.352587i	$-0.114698\pi$
$421$	−0.585339	−	1.80149i	−0.0285277	−	0.0877991i	−0.964307	+	0.264788i	$0.914698\pi$
$422$	3.58264	−	11.0262i	0.174400	−	0.536748i
$423$		0			0
$424$	−3.56854	−	2.59270i	−0.173304	−	0.125913i
$425$	2.05594	−	6.32755i	0.0997280	−	0.306931i
$426$		0			0
$427$	40.4694	−	29.4027i	1.95845	−	1.42290i
$428$	−7.26581			−0.351206
$429$		0			0
$430$	−2.86473			−0.138149
$431$	1.23007	−	0.893702i	0.0592506	−	0.0430481i	−0.557766	−	0.829998i	$-0.688341\pi$
$431$	1.23007	−	0.893702i	0.0592506	−	0.0430481i	0.617016	+	0.786950i	$0.288341\pi$
$432$		0			0
$433$	8.48671	−	26.1194i	0.407845	−	1.25522i	−0.510651	−	0.859788i	$-0.670596\pi$
$433$	8.48671	−	26.1194i	0.407845	−	1.25522i	0.918496	−	0.395430i	$-0.129404\pi$
$434$	−21.7137	−	15.7759i	−1.04229	−	0.757269i
$435$		0			0
$436$	−1.75819	+	5.41114i	−0.0842019	+	0.259147i
$437$	4.83478	+	14.8799i	0.231279	+	0.711803i
$438$		0			0
$439$	3.87089			0.184748			0.0923738	−	0.995724i	$-0.470555\pi$
$439$	3.87089			0.184748			0.0923738	+	0.995724i	$0.470555\pi$
$440$	2.19536	−	2.07308i	0.104659	−	0.0988304i
$441$		0			0
$442$	−5.04495	+	3.66537i	−0.239964	+	0.174344i
$443$	−11.5131	−	35.4336i	−0.547002	−	1.68350i	−0.716182	−	0.697914i	$-0.754112\pi$
$443$	−11.5131	−	35.4336i	−0.547002	−	1.68350i	0.169180	−	0.985585i	$-0.445888\pi$
$444$		0			0
$445$	3.92147	+	2.84912i	0.185896	+	0.135061i
$446$	−15.1553	−	11.0110i	−0.717623	−	0.521384i
$447$		0			0
$448$	11.7638	+	36.2053i	0.555788	+	1.71054i
$449$	−14.5946	+	10.6036i	−0.688761	+	0.500414i	−0.876253	−	0.481852i	$-0.839964\pi$
$449$	−14.5946	+	10.6036i	−0.688761	+	0.500414i	0.187492	+	0.982266i	$0.439964\pi$
$450$		0			0
$451$	3.72197	−	19.8101i	0.175261	−	0.932822i
$452$	−2.71512			−0.127709
$453$		0			0
$454$	7.69315	+	23.6771i	0.361057	+	1.11122i
$455$	−1.49242	+	4.59320i	−0.0699658	+	0.215332i
$456$		0			0
$457$	14.6325	+	10.6312i	0.684481	+	0.497304i	0.874841	−	0.484410i	$-0.160966\pi$
$457$	14.6325	+	10.6312i	0.684481	+	0.497304i	−0.190360	+	0.981714i	$0.560966\pi$
$458$	−10.9859	+	33.8111i	−0.513337	+	1.57989i
$459$		0			0
$460$	0.593956	−	0.431534i	0.0276933	−	0.0201204i
$461$	−12.2841			−0.572128			−0.286064	−	0.958210i	$-0.592347\pi$
$461$	−12.2841			−0.572128			−0.286064	+	0.958210i	$0.592347\pi$
$462$		0			0
$463$	0.168090			0.00781181			0.00390590	−	0.999992i	$-0.498757\pi$
$463$	0.168090			0.00781181			0.00390590	+	0.999992i	$0.498757\pi$
$464$	21.8014	−	15.8396i	1.01210	−	0.735337i
$465$		0			0
$466$	0.275225	−	0.847054i	0.0127495	−	0.0392390i
$467$	−4.30387	−	3.12694i	−0.199159	−	0.144698i	0.483736	−	0.875214i	$-0.339279\pi$
$467$	−4.30387	−	3.12694i	−0.199159	−	0.144698i	−0.682895	+	0.730516i	$0.739279\pi$
$468$		0			0
$469$	−3.56360	+	10.9676i	−0.164552	+	0.506439i
$470$	0.534142	+	1.64392i	0.0246381	+	0.0758283i
$471$		0			0
$472$	−19.3768			−0.891889
$473$	23.0804	+	12.6052i	1.06124	+	0.579588i
$474$		0			0
$475$	13.0744	−	9.49912i	0.599895	−	0.435849i
$476$	0.935239	+	2.87837i	0.0428666	+	0.131930i
$477$		0			0
$478$	22.7948	+	16.5614i	1.04261	+	0.757500i
$479$	−19.4643	−	14.1416i	−0.889347	−	0.646148i	0.0463610	−	0.998925i	$-0.485238\pi$
$479$	−19.4643	−	14.1416i	−0.889347	−	0.646148i	−0.935708	+	0.352777i	$0.885238\pi$
$480$		0			0
$481$	−5.29834	−	16.3066i	−0.241583	−	0.743517i
$482$	2.56275	−	1.86195i	0.116730	−	0.0848095i
$483$		0			0
$484$	−5.53121	+	1.45298i	−0.251419	+	0.0660447i
$485$	1.15942			0.0526465
$486$		0			0
$487$	−12.1041	−	37.2526i	−0.548490	−	1.68808i	−0.712544	−	0.701627i	$-0.752457\pi$
$487$	−12.1041	−	37.2526i	−0.548490	−	1.68808i	0.164055	−	0.986451i	$-0.447543\pi$
$488$	11.0267	−	33.9366i	0.499154	−	1.53624i
$489$		0			0
$490$	−3.35259	−	2.43580i	−0.151455	−	0.110038i
$491$	−5.39016	+	16.5892i	−0.243255	+	0.748661i	0.752664	+	0.658405i	$0.228769\pi$
$491$	−5.39016	+	16.5892i	−0.243255	+	0.748661i	−0.995919	+	0.0902561i	$0.971231\pi$
$492$		0			0
$493$	10.9783	−	7.97618i	0.494436	−	0.359229i
$494$	−15.1473			−0.681509
$495$		0			0
$496$	−13.8081			−0.620001
$497$	−22.2346	+	16.1544i	−0.997356	+	0.724622i
$498$		0			0
$499$	2.21880	−	6.82878i	0.0993273	−	0.305698i	−0.889030	−	0.457849i	$-0.848620\pi$
$499$	2.21880	−	6.82878i	0.0993273	−	0.305698i	0.988357	+	0.152151i	$0.0486200\pi$
$500$	−1.23804	−	0.899490i	−0.0553669	−	0.0402264i
$501$		0			0
$502$	7.58434	−	23.3422i	0.338505	−	1.04181i
$503$	−1.95460	−	6.01565i	−0.0871515	−	0.268225i	0.897977	−	0.440042i	$-0.145036\pi$
$503$	−1.95460	−	6.01565i	−0.0871515	−	0.268225i	−0.985129	+	0.171817i	$0.945036\pi$
$504$		0			0
$505$	−3.21038			−0.142860
$506$	19.0292	−	2.45769i	0.845953	−	0.109257i
$507$		0			0
$508$	−0.632457	+	0.459507i	−0.0280607	+	0.0203873i
$509$	4.71879	+	14.5229i	0.209157	+	0.643718i	0.999517	+	0.0310758i	$0.00989334\pi$
$509$	4.71879	+	14.5229i	0.209157	+	0.643718i	−0.790360	+	0.612642i	$0.790107\pi$
$510$		0			0
$511$	−5.75250	−	4.17943i	−0.254475	−	0.184887i
$512$	19.5644	+	14.2144i	0.864634	+	0.628193i
$513$		0			0
$514$	−3.25078	−	10.0049i	−0.143386	−	0.441296i
$515$	−1.05468	+	0.766270i	−0.0464748	+	0.0337659i
$516$		0			0
$517$	2.93002	−	15.5950i	0.128862	−	0.685866i
$518$	23.6904			1.04090
$519$		0			0
$520$	1.06460	+	3.27649i	0.0466856	+	0.143683i
$521$	−3.54599	+	10.9134i	−0.155353	+	0.478126i	−0.998196	−	0.0600320i	$-0.980880\pi$
$521$	−3.54599	+	10.9134i	−0.155353	+	0.478126i	0.842844	+	0.538158i	$0.180880\pi$
$522$		0			0
$523$	16.0982	+	11.6960i	0.703924	+	0.511431i	0.881208	−	0.472729i	$-0.156731\pi$
$523$	16.0982	+	11.6960i	0.703924	+	0.511431i	−0.177284	+	0.984160i	$0.556731\pi$
$524$	−3.10914	+	9.56896i	−0.135824	+	0.418022i
$525$		0			0
$526$	−22.0651	+	16.0312i	−0.962083	+	0.698994i
$527$	−6.95316			−0.302884
$528$		0			0
$529$	−0.387783			−0.0168601
$530$	0.420548	−	0.305546i	0.0182674	−	0.0132721i
$531$		0			0
$532$	−2.27174	+	6.99169i	−0.0984924	+	0.303128i
$533$	18.6058	+	13.5179i	0.805905	+	0.585525i
$534$		0			0
$535$	1.28250	−	3.94712i	0.0554471	−	0.170649i
$536$	2.54204	+	7.82360i	0.109799	+	0.337928i
$537$		0			0
$538$	−4.69513			−0.202421
$539$	16.2932	+	34.3765i	0.701797	+	1.48070i
$540$		0			0
$541$	−5.78434	+	4.20257i	−0.248688	+	0.180683i	−0.705145	−	0.709063i	$-0.749118\pi$
$541$	−5.78434	+	4.20257i	−0.248688	+	0.180683i	0.456457	+	0.889745i	$0.349118\pi$
$542$	−11.7142	−	36.0525i	−0.503166	−	1.54859i
$543$		0			0
$544$	3.13283	+	2.27614i	0.134319	+	0.0975885i
$545$	−2.62924	−	1.91025i	−0.112624	−	0.0818262i
$546$		0			0
$547$	−4.99139	−	15.3619i	−0.213416	−	0.656828i	−0.999262	−	0.0384055i	$-0.987772\pi$
$547$	−4.99139	−	15.3619i	−0.213416	−	0.656828i	0.785846	−	0.618422i	$-0.212228\pi$
$548$	−8.44712	+	6.13720i	−0.360843	+	0.262168i
$549$		0			0
$550$	−8.48835	−	17.9093i	−0.361945	−	0.763657i
$551$	32.9619			1.40422
$552$		0			0
$553$	9.06661	+	27.9041i	0.385551	+	1.18660i
$554$	3.91031	−	12.0347i	0.166133	−	0.511305i
$555$		0			0
$556$	5.17932	+	3.76300i	0.219652	+	0.159587i
$557$	11.0591	−	34.0364i	0.468589	−	1.44217i	−0.385823	−	0.922573i	$-0.626082\pi$
$557$	11.0591	−	34.0364i	0.468589	−	1.44217i	0.854412	−	0.519596i	$-0.173918\pi$
$558$		0			0
$559$	−24.2747	+	17.6366i	−1.02671	+	0.745950i
$560$	−3.43305			−0.145073
$561$		0			0
$562$	10.4122			0.439210
$563$	10.5553	−	7.66889i	0.444854	−	0.323205i	−0.342707	−	0.939442i	$-0.611344\pi$
$563$	10.5553	−	7.66889i	0.444854	−	0.323205i	0.787561	+	0.616237i	$0.211344\pi$
$564$		0			0
$565$	0.479249	−	1.47498i	0.0201622	−	0.0620528i
$566$	3.59664	+	2.61311i	0.151178	+	0.109837i
$567$		0			0
$568$	−6.05824	+	18.6453i	−0.254198	+	0.782341i
$569$	−8.75620	−	26.9488i	−0.367079	−	1.12975i	−0.948669	−	0.316271i	$-0.897569\pi$
$569$	−8.75620	−	26.9488i	−0.367079	−	1.12975i	0.581590	−	0.813482i	$-0.302431\pi$
$570$		0			0
$571$	−30.3427			−1.26980			−0.634901	−	0.772593i	$-0.718959\pi$
$571$	−30.3427			−1.26980			−0.634901	+	0.772593i	$0.718959\pi$
$572$	1.20485	−	6.41279i	0.0503773	−	0.268132i
$573$		0			0
$574$	−25.7077	+	18.6777i	−1.07302	+	0.779593i
$575$	−7.21765	−	22.2136i	−0.300997	−	0.926372i
$576$		0			0
$577$	13.4456	+	9.76878i	0.559747	+	0.406680i	0.831366	−	0.555725i	$-0.187559\pi$
$577$	13.4456	+	9.76878i	0.559747	+	0.406680i	−0.271620	+	0.962405i	$0.587559\pi$
$578$	14.9263	+	10.8446i	0.620854	+	0.451077i
$579$		0			0
$580$	−0.477965	−	1.47102i	−0.0198464	−	0.0610810i
$581$	−17.5724	+	12.7671i	−0.729027	+	0.529669i
$582$		0			0
$583$	−4.73270	+	0.611243i	−0.196008	+	0.0253151i
$584$	−5.07215			−0.209887
$585$		0			0
$586$	2.42976	+	7.47805i	0.100373	+	0.308915i
$587$	−4.13339	+	12.7213i	−0.170603	+	0.525062i	−0.999405	−	0.0344792i	$-0.989023\pi$
$587$	−4.13339	+	12.7213i	−0.170603	+	0.525062i	0.828802	+	0.559542i	$0.189023\pi$
$588$		0			0
$589$	−13.6639	−	9.92742i	−0.563012	−	0.409052i
$590$	0.705649	−	2.17176i	0.0290511	−	0.0894101i
$591$		0			0
$592$	9.86022	−	7.16387i	0.405253	−	0.294433i
$593$	15.8491			0.650843			0.325422	−	0.945569i	$-0.394494\pi$
$593$	15.8491			0.650843			0.325422	+	0.945569i	$0.394494\pi$
$594$		0			0
$595$	−1.72874			−0.0708715
$596$	5.34260	−	3.88162i	0.218841	−	0.158998i
$597$		0			0
$598$	−6.76497	+	20.8205i	−0.276640	+	0.851412i
$599$	12.6046	+	9.15776i	0.515009	+	0.374176i	0.814721	−	0.579854i	$-0.196890\pi$
$599$	12.6046	+	9.15776i	0.515009	+	0.374176i	−0.299711	+	0.954030i	$0.596890\pi$
$600$		0			0
$601$	1.78207	−	5.48465i	0.0726922	−	0.223724i	−0.908109	−	0.418734i	$-0.862474\pi$
$601$	1.78207	−	5.48465i	0.0726922	−	0.223724i	0.980801	+	0.195010i	$0.0624740\pi$
$602$	−12.8113	−	39.4292i	−0.522151	−	1.60701i
$603$		0			0
$604$	3.59355			0.146220
$605$	0.186994	−	3.26127i	0.00760239	−	0.132590i
$606$		0			0
$607$	19.6406	−	14.2698i	0.797189	−	0.579192i	−0.112899	−	0.993606i	$-0.536014\pi$
$607$	19.6406	−	14.2698i	0.797189	−	0.579192i	0.910088	+	0.414415i	$0.136014\pi$
$608$	2.90668	+	8.94585i	0.117881	+	0.362802i
$609$		0			0
$610$	3.40208	+	2.47175i	0.137746	+	0.100078i
$611$	14.6469	+	10.6416i	0.592549	+	0.430512i
$612$		0			0
$613$	8.35427	+	25.7118i	0.337426	+	1.03849i	0.965515	+	0.260348i	$0.0838373\pi$
$613$	8.35427	+	25.7118i	0.337426	+	1.03849i	−0.628089	+	0.778141i	$0.716163\pi$
$614$	−24.4342	+	17.7525i	−0.986086	+	0.716433i
$615$		0			0
$616$	38.3511	+	20.9451i	1.54521	+	0.843904i
$617$	28.6135			1.15193			0.575967	−	0.817473i	$-0.304626\pi$
$617$	28.6135			1.15193			0.575967	+	0.817473i	$0.304626\pi$
$618$		0			0
$619$	−9.95700	−	30.6445i	−0.400205	−	1.23171i	−0.924833	−	0.380374i	$-0.875795\pi$
$619$	−9.95700	−	30.6445i	−0.400205	−	1.23171i	0.524627	−	0.851332i	$-0.324205\pi$
$620$	−0.244908	+	0.753748i	−0.00983572	+	0.0302712i
$621$		0			0
$622$	9.27274	+	6.73704i	0.371803	+	0.270131i
$623$	−21.6771	+	66.7154i	−0.868476	+	2.67290i
$624$		0			0
$625$	−19.1615	+	13.9217i	−0.766461	+	0.556866i
$626$	−22.5588			−0.901631
$627$		0			0
$628$	−3.41725			−0.136363
$629$	4.96519	−	3.60742i	0.197975	−	0.143837i
$630$		0			0
$631$	−4.62443	+	14.2325i	−0.184096	+	0.566588i	−0.999932	−	0.0116954i	$-0.996277\pi$
$631$	−4.62443	+	14.2325i	−0.184096	+	0.566588i	0.815836	+	0.578283i	$0.196277\pi$
$632$	16.9322	+	12.3020i	0.673527	+	0.489346i
$633$		0			0
$634$	−2.10287	+	6.47196i	−0.0835156	+	0.257034i
$635$	−0.137989	−	0.424687i	−0.00547593	−	0.0168532i
$636$		0			0
$637$	−43.4046			−1.71975
$638$	7.46421	−	39.7281i	0.295511	−	1.57285i
$639$		0			0
$640$	−1.21537	+	0.883018i	−0.0480417	+	0.0349043i
$641$	4.66108	+	14.3453i	0.184102	+	0.566606i	0.999932	−	0.0116853i	$-0.00371962\pi$
$641$	4.66108	+	14.3453i	0.184102	+	0.566606i	−0.815830	+	0.578292i	$0.803720\pi$
$642$		0			0
$643$	−19.1204	−	13.8918i	−0.754034	−	0.547838i	0.143041	−	0.989717i	$-0.454312\pi$
$643$	−19.1204	−	13.8918i	−0.754034	−	0.547838i	−0.897075	+	0.441879i	$0.854312\pi$
$644$	8.59572	+	6.24516i	0.338719	+	0.246094i
$645$		0			0
$646$	−1.67548	−	5.15659i	−0.0659208	−	0.202883i
$647$	3.66443	−	2.66236i	0.144064	−	0.104668i	−0.513419	−	0.858138i	$-0.671621\pi$
$647$	3.66443	−	2.66236i	0.144064	−	0.104668i	0.657483	+	0.753470i	$0.271621\pi$
$648$		0			0
$649$	−15.2413	+	14.3924i	−0.598273	+	0.564952i
$650$	22.6128			0.886946
$651$		0			0
$652$	−0.517487	−	1.59266i	−0.0202664	−	0.0623735i
$653$	0.260750	−	0.802506i	0.0102039	−	0.0314045i	−0.945825	−	0.324677i	$-0.894744\pi$
$653$	0.260750	−	0.802506i	0.0102039	−	0.0314045i	0.956029	+	0.293273i	$0.0947444\pi$
$654$		0			0
$655$	−4.64949	−	3.37805i	−0.181671	−	0.131991i
$656$	−5.05178	+	15.5478i	−0.197239	+	0.607038i
$657$		0			0
$658$	−20.2376	+	14.7035i	−0.788946	+	0.573202i
$659$	−17.7262			−0.690515			−0.345257	−	0.938508i	$-0.612208\pi$
$659$	−17.7262			−0.690515			−0.345257	+	0.938508i	$0.612208\pi$
$660$		0			0
$661$	−40.9606			−1.59318			−0.796592	−	0.604518i	$-0.793366\pi$
$661$	−40.9606			−1.59318			−0.796592	+	0.604518i	$0.793366\pi$
$662$	−19.1799	+	13.9350i	−0.745448	+	0.541600i
$663$		0			0
$664$	−4.78795	+	14.7358i	−0.185809	+	0.571860i
$665$	−3.39722	−	2.46822i	−0.131738	−	0.0957135i
$666$		0			0
$667$	14.7212	−	45.3071i	0.570006	−	1.75430i
$668$	−1.67918	−	5.16799i	−0.0649695	−	0.199956i
$669$		0			0
$670$	−0.969448			−0.0374530
$671$	−16.5337	−	34.8839i	−0.638275	−	1.34668i
$672$		0			0
$673$	−7.38179	+	5.36319i	−0.284547	+	0.206736i	−0.720898	−	0.693041i	$-0.756271\pi$
$673$	−7.38179	+	5.36319i	−0.284547	+	0.206736i	0.436351	+	0.899776i	$0.356271\pi$
$674$	4.68225	+	14.4105i	0.180353	+	0.555071i
$675$		0			0
$676$	0.555055	+	0.403271i	0.0213483	+	0.0155104i
$677$	−24.9222	−	18.1070i	−0.957837	−	0.695909i	−0.00518928	−	0.999987i	$-0.501652\pi$
$677$	−24.9222	−	18.1070i	−0.957837	−	0.695909i	−0.952647	+	0.304078i	$0.901652\pi$
$678$		0			0
$679$	5.18503	+	15.9579i	0.198983	+	0.612407i
$680$	−0.997656	+	0.724840i	−0.0382584	+	0.0277963i
$681$		0			0
$682$	−15.0595	+	14.2207i	−0.576657	+	0.544540i
$683$	27.4084			1.04875			0.524377	−	0.851486i	$-0.324298\pi$
$683$	27.4084			1.04875			0.524377	+	0.851486i	$0.324298\pi$
$684$		0			0
$685$	−1.84299	−	5.67214i	−0.0704170	−	0.216721i
$686$	7.22250	−	22.2286i	0.275756	−	0.848690i
$687$		0			0
$688$	−17.2554	−	12.5368i	−0.657858	−	0.477962i
$689$	1.68249	−	5.17818i	0.0640979	−	0.197273i
$690$		0			0
$691$	−1.45541	+	1.05742i	−0.0553664	+	0.0402261i	−0.615124	−	0.788430i	$-0.710894\pi$
$691$	−1.45541	+	1.05742i	−0.0553664	+	0.0402261i	0.559758	+	0.828656i	$0.310894\pi$
$692$	−6.89694			−0.262182
$693$		0			0
$694$	−17.8104			−0.676074
$695$	−2.95844	+	2.14943i	−0.112220	+	0.0815325i
$696$		0			0
$697$	−2.54386	+	7.82920i	−0.0963556	+	0.296552i
$698$	19.6600	+	14.2838i	0.744141	+	0.540650i
$699$		0			0
$700$	3.39138	−	10.4376i	0.128182	−	0.394505i
$701$	−3.16366	−	9.73676i	−0.119490	−	0.367752i	0.873367	−	0.487063i	$-0.161932\pi$
$701$	−3.16366	−	9.73676i	−0.119490	−	0.367752i	−0.992857	+	0.119310i	$0.961932\pi$
$702$		0			0
$703$	14.9078			0.562259
$704$	29.1363	−	3.76304i	1.09812	−	0.141825i
$705$		0			0
$706$	28.1079	−	20.4216i	1.05785	−	0.768576i
$707$	−14.3571	−	44.1867i	−0.539956	−	1.66181i
$708$		0			0
$709$	−18.3375	−	13.3230i	−0.688679	−	0.500354i	0.187547	−	0.982256i	$-0.439946\pi$
$709$	−18.3375	−	13.3230i	−0.688679	−	0.500354i	−0.876226	+	0.481901i	$0.839946\pi$
$710$	−1.86916	−	1.35802i	−0.0701483	−	0.0509657i
$711$		0			0
$712$	15.4631	+	47.5904i	0.579503	+	1.78353i
$713$	−19.7480	+	14.3478i	−0.739570	+	0.537329i
$714$		0			0
$715$	3.27105	+	1.78646i	0.122330	+	0.0668097i
$716$	−10.1948			−0.380999
$717$		0			0
$718$	−4.65356	−	14.3222i	−0.173669	−	0.534499i
$719$	−11.6978	+	36.0023i	−0.436256	+	1.34266i	0.455538	+	0.890216i	$0.349447\pi$
$719$	−11.6978	+	36.0023i	−0.436256	+	1.34266i	−0.891794	+	0.452441i	$0.850553\pi$
$720$		0			0
$721$	−15.2633	−	11.0895i	−0.568436	−	0.412993i
$722$	−3.07321	+	9.45837i	−0.114373	+	0.352004i
$723$		0			0
$724$	−10.7815	+	7.83321i	−0.400691	+	0.291119i
$725$	−49.2074			−1.82752
$726$		0			0
$727$	16.6183			0.616339			0.308169	−	0.951332i	$-0.400284\pi$
$727$	16.6183			0.616339			0.308169	+	0.951332i	$0.400284\pi$
$728$	−40.3356	+	29.3055i	−1.49494	+	1.08613i
$729$		0			0
$730$	0.184714	−	0.568490i	0.00683656	−	0.0210408i
$731$	−8.68911	−	6.31301i	−0.321378	−	0.233495i
$732$		0			0
$733$	8.58415	−	26.4193i	0.317063	−	0.975819i	−0.657834	−	0.753163i	$-0.728527\pi$
$733$	8.58415	−	26.4193i	0.317063	−	0.975819i	0.974897	−	0.222656i	$-0.0714728\pi$
$734$	−9.18177	−	28.2586i	−0.338905	−	1.04304i
$735$		0			0
$736$	13.5945			0.501100
$737$	7.81061	+	4.26570i	0.287708	+	0.157129i
$738$		0			0
$739$	−3.84927	+	2.79666i	−0.141598	+	0.102877i	−0.656329	−	0.754475i	$-0.727892\pi$
$739$	−3.84927	+	2.79666i	−0.141598	+	0.102877i	0.514731	+	0.857352i	$0.327892\pi$
$740$	−0.216171	−	0.665307i	−0.00794662	−	0.0244572i
$741$		0			0
$742$	6.08616	+	4.42186i	0.223430	+	0.162331i
$743$	−31.5327	−	22.9099i	−1.15682	−	0.840482i	−0.167451	−	0.985880i	$-0.553554\pi$
$743$	−31.5327	−	22.9099i	−1.15682	−	0.840482i	−0.989373	+	0.145398i	$0.953554\pi$
$744$		0			0
$745$	1.16565	+	3.58749i	0.0427060	+	0.131435i
$746$	−3.08440	+	2.24095i	−0.112928	+	0.0820469i
$747$		0			0
$748$	2.31638	−	0.299167i	0.0846951	−	0.0109386i
$749$	60.0623			2.19463
$750$		0			0
$751$	14.9389	+	45.9773i	0.545129	+	1.67774i	0.720682	+	0.693266i	$0.243829\pi$
$751$	14.9389	+	45.9773i	0.545129	+	1.67774i	−0.175552	+	0.984470i	$0.556171\pi$
$752$	−3.97687	+	12.2395i	−0.145022	+	0.446330i
$753$		0			0
$754$	37.3129	+	27.1094i	1.35885	+	0.987266i
$755$	−0.634302	+	1.95218i	−0.0230846	+	0.0710471i
$756$		0			0
$757$	−37.7757	+	27.4457i	−1.37298	+	0.997529i	−0.375483	+	0.926829i	$0.622523\pi$
$757$	−37.7757	+	27.4457i	−1.37298	+	0.997529i	−0.997498	+	0.0707000i	$0.977477\pi$
$758$	20.3273			0.738320
$759$		0			0
$760$	−2.99543			−0.108656
$761$	−4.76285	+	3.46042i	−0.172653	+	0.125440i	−0.670756	−	0.741678i	$-0.734030\pi$
$761$	−4.76285	+	3.46042i	−0.172653	+	0.125440i	0.498103	+	0.867118i	$0.334030\pi$
$762$		0			0
$763$	14.5339	−	44.7308i	0.526163	−	1.61936i
$764$	−6.47815	−	4.70665i	−0.234371	−	0.170281i
$765$		0			0
$766$	−2.57663	+	7.93007i	−0.0930976	+	0.286525i
$767$	−7.39098	−	22.7471i	−0.266873	−	0.821350i
$768$		0			0
$769$	37.1729			1.34049			0.670245	−	0.742140i	$-0.266189\pi$
$769$	37.1729			1.34049			0.670245	+	0.742140i	$0.266189\pi$
$770$	−3.74419	+	3.53565i	−0.134931	+	0.127416i
$771$		0			0
$772$	−5.92667	+	4.30598i	−0.213306	+	0.154976i
$773$	1.81396	+	5.58279i	0.0652435	+	0.200799i	0.978364	−	0.206891i	$-0.0663345\pi$
$773$	1.81396	+	5.58279i	0.0652435	+	0.200799i	−0.913121	+	0.407690i	$0.866335\pi$
$774$		0			0
$775$	20.3983	+	14.8202i	0.732729	+	0.532359i
$776$	9.68322	+	7.03527i	0.347607	+	0.252552i
$777$		0			0
$778$	−8.97137	−	27.6110i	−0.321639	−	0.989903i
$779$	−16.1772	+	11.7534i	−0.579610	+	0.421111i
$780$		0			0
$781$	9.08388	+	19.1658i	0.325047	+	0.685807i
$782$	−7.83619			−0.280222
$783$		0			0
$784$	−9.53433	−	29.3436i	−0.340512	−	1.04799i
$785$	0.603182	−	1.85640i	0.0215285	−	0.0662579i
$786$		0			0
$787$	6.19242	+	4.49905i	0.220736	+	0.160374i	0.692658	−	0.721266i	$-0.256440\pi$
$787$	6.19242	+	4.49905i	0.220736	+	0.160374i	−0.471922	+	0.881640i	$0.656440\pi$
$788$	0.825868	−	2.54176i	0.0294203	−	0.0905464i
$789$		0			0
$790$	−1.99544	+	1.44977i	−0.0709944	+	0.0515805i
$791$	22.4444			0.798030
$792$		0			0
$793$	44.0453			1.56410
$794$	2.45110	−	1.78083i	0.0869863	−	0.0631992i
$795$		0			0
$796$	2.56345	−	7.88950i	0.0908592	−	0.279636i
$797$	26.4082	+	19.1867i	0.935426	+	0.679627i	0.947315	−	0.320302i	$-0.103785\pi$
$797$	26.4082	+	19.1867i	0.935426	+	0.679627i	−0.0118892	+	0.999929i	$0.503785\pi$
$798$		0			0
$799$	−2.00258	+	6.16332i	−0.0708463	+	0.218043i
$800$	−4.33926	−	13.3549i	−0.153416	−	0.472166i
$801$		0			0
$802$	−25.6650			−0.906264
$803$	−3.98963	+	3.76742i	−0.140791	+	0.132949i
$804$		0			0
$805$	−4.90989	+	3.56724i	−0.173051	+	0.125729i
$806$	−7.30280	−	22.4757i	−0.257230	−	0.791673i
$807$		0			0
$808$	−26.8124	−	19.4804i	−0.943258	−	0.685317i
$809$	−23.1264	−	16.8023i	−0.813083	−	0.590739i	0.101640	−	0.994821i	$-0.467591\pi$
$809$	−23.1264	−	16.8023i	−0.813083	−	0.590739i	−0.914723	+	0.404082i	$0.867591\pi$
$810$		0			0
$811$	−3.88616	−	11.9604i	−0.136461	−	0.419985i	0.859353	−	0.511383i	$-0.170867\pi$
$811$	−3.88616	−	11.9604i	−0.136461	−	0.419985i	−0.995814	+	0.0913977i	$0.970867\pi$
$812$	18.1092	−	13.1571i	0.635509	−	0.461724i
$813$		0			0
$814$	3.37587	−	17.9680i	0.118324	−	0.629779i
$815$	0.956548			0.0335064
$816$		0			0
$817$	−8.06187	−	24.8119i	−0.282049	−	0.868058i
$818$	−5.72360	+	17.6154i	−0.200121	+	0.615909i
$819$		0			0
$820$	0.759113	+	0.551528i	0.0265094	+	0.0192602i
$821$	−8.35458	+	25.7128i	−0.291577	+	0.897382i	0.692773	+	0.721156i	$0.256389\pi$
$821$	−8.35458	+	25.7128i	−0.291577	+	0.897382i	−0.984350	+	0.176226i	$0.943611\pi$
$822$		0			0
$823$	−5.50194	+	3.99739i	−0.191786	+	0.139340i	−0.679534	−	0.733644i	$-0.737818\pi$
$823$	−5.50194	+	3.99739i	−0.191786	+	0.139340i	0.487749	+	0.872984i	$0.337818\pi$
$824$	−13.4581			−0.468837
$825$		0			0
$826$	33.0472			1.14986
$827$	22.6938	−	16.4880i	0.789142	−	0.573345i	−0.118566	−	0.992946i	$-0.537830\pi$
$827$	22.6938	−	16.4880i	0.789142	−	0.573345i	0.907709	+	0.419601i	$0.137830\pi$
$828$		0			0
$829$	15.9591	−	49.1170i	0.554282	−	1.70591i	−0.143549	−	0.989643i	$-0.545852\pi$
$829$	15.9591	−	49.1170i	0.554282	−	1.70591i	0.697831	−	0.716262i	$-0.254148\pi$
$830$	−1.47723	−	1.07327i	−0.0512755	−	0.0372539i
$831$		0			0
$832$	−10.3581	+	31.8789i	−0.359102	+	1.10520i
$833$	−4.80109	−	14.7762i	−0.166348	−	0.511966i
$834$		0			0
$835$	3.10388			0.107414
$836$	4.97914	+	2.71932i	0.172207	+	0.0940495i
$837$		0			0
$838$	−2.29442	+	1.66699i	−0.0792593	+	0.0575853i
$839$	5.26790	+	16.2129i	0.181868	+	0.559732i	0.999880	−	0.0154686i	$-0.00492400\pi$
$839$	5.26790	+	16.2129i	0.181868	+	0.559732i	−0.818012	+	0.575201i	$0.804924\pi$
$840$		0			0
$841$	−57.7346	−	41.9467i	−1.99085	−	1.44644i
$842$	1.86435	+	1.35453i	0.0642499	+	0.0466803i
$843$		0			0
$844$	−1.53100	−	4.71192i	−0.0526991	−	0.162191i
$845$	−0.317049	+	0.230349i	−0.0109068	+	0.00792426i
$846$		0			0
$847$	45.7234	−	12.0110i	1.57107	−	0.412702i
$848$	3.87028			0.132906
$849$		0			0
$850$	2.50125	+	7.69806i	0.0857922	+	0.264041i
$851$	6.65802	−	20.4913i	0.228234	−	0.702432i
$852$		0			0
$853$	16.1838	+	11.7582i	0.554122	+	0.402594i	0.829303	−	0.558799i	$-0.188738\pi$
$853$	16.1838	+	11.7582i	0.554122	+	0.402594i	−0.275181	+	0.961393i	$0.588738\pi$
$854$	−18.8060	+	57.8790i	−0.643529	+	1.98058i
$855$		0			0
$856$	34.6619	−	25.1834i	1.18472	−	0.860750i
$857$	19.3076			0.659536			0.329768	−	0.944062i	$-0.393029\pi$
$857$	19.3076			0.659536			0.329768	+	0.944062i	$0.393029\pi$
$858$		0			0
$859$	21.7196			0.741063			0.370531	−	0.928820i	$-0.379176\pi$
$859$	21.7196			0.741063			0.370531	+	0.928820i	$0.379176\pi$
$860$	−0.990405	+	0.719571i	−0.0337725	+	0.0245372i
$861$		0			0
$862$	−0.571613	+	1.75924i	−0.0194692	+	0.0599201i
$863$	11.0445	+	8.02429i	0.375959	+	0.273150i	0.759677	−	0.650300i	$-0.225357\pi$
$863$	11.0445	+	8.02429i	0.375959	+	0.273150i	−0.383719	+	0.923450i	$0.625357\pi$
$864$		0			0
$865$	1.21739	−	3.74673i	0.0413924	−	0.127393i
$866$	10.3249	+	31.7767i	0.350854	+	1.07982i
$867$		0			0
$868$	−11.4696			−0.389303
$869$	22.4559	−	2.90025i	0.761765	−	0.0983844i
$870$		0			0
$871$	−8.21477	+	5.96838i	−0.278347	+	0.202231i
$872$	−10.3676	−	31.9080i	−0.351090	−	1.08054i
$873$		0			0
$874$	−15.3992	−	11.1882i	−0.520886	−	0.378446i
$875$	10.2342	+	7.43557i	0.345979	+	0.251368i
$876$		0			0
$877$	−3.67201	−	11.3013i	−0.123995	−	0.381617i	0.869722	−	0.493543i	$-0.164298\pi$
$877$	−3.67201	−	11.3013i	−0.123995	−	0.381617i	−0.993717	+	0.111925i	$0.964298\pi$
$878$	−3.80991	+	2.76806i	−0.128578	+	0.0934175i
$879$		0			0
$880$	−0.489209	+	2.60381i	−0.0164912	+	0.0877743i
$881$	41.6730			1.40400			0.702000	−	0.712177i	$-0.252291\pi$
$881$	41.6730			1.40400			0.702000	+	0.712177i	$0.252291\pi$
$882$		0			0
$883$	2.74739	+	8.45560i	0.0924570	+	0.284553i	0.986583	−	0.163263i	$-0.0522018\pi$
$883$	2.74739	+	8.45560i	0.0924570	+	0.284553i	−0.894126	+	0.447816i	$0.852202\pi$
$884$	−0.823481	+	2.53441i	−0.0276967	+	0.0852416i
$885$		0			0
$886$	36.6701	+	26.6424i	1.23196	+	0.895068i
$887$	5.88464	−	18.1111i	0.197587	−	0.608110i	−0.802350	−	0.596854i	$-0.796417\pi$
$887$	5.88464	−	18.1111i	0.197587	−	0.608110i	0.999937	−	0.0112557i	$-0.00358287\pi$
$888$		0			0
$889$	5.22816	−	3.79848i	0.175347	−	0.127397i
$890$	−5.89708			−0.197671
$891$		0			0
$892$	−8.00531			−0.268038
$893$	−12.7351	+	9.25257i	−0.426163	+	0.309626i
$894$		0			0
$895$	1.79950	−	5.53829i	0.0601507	−	0.185125i
$896$	−17.5888	−	12.7790i	−0.587601	−	0.426917i
$897$		0			0
$898$	6.78207	−	20.8731i	0.226321	−	0.696543i
$899$	15.8915	+	48.9091i	0.530013	+	1.63121i
$900$		0			0
$901$	1.94891			0.0649276
$902$	10.5028	+	22.1596i	0.349705	+	0.737834i
$903$		0			0
$904$	12.9526	−	9.41065i	0.430798	−	0.312993i
$905$	−2.35230	−	7.23964i	−0.0781932	−	0.240654i
$906$		0			0
$907$	45.0291	+	32.7156i	1.49517	+	1.08630i	0.972257	+	0.233915i	$0.0751537\pi$
$907$	45.0291	+	32.7156i	1.49517	+	1.08630i	0.522910	+	0.852388i	$0.324846\pi$
$908$	8.60699	+	6.25334i	0.285633	+	0.207524i
$909$		0			0
$910$	−1.81567	−	5.58806i	−0.0601889	−	0.185242i
$911$	14.8068	−	10.7578i	0.490572	−	0.356421i	−0.314832	−	0.949147i	$-0.601948\pi$
$911$	14.8068	−	10.7578i	0.490572	−	0.356421i	0.805404	+	0.592726i	$0.201948\pi$
$912$		0			0
$913$	7.17917	+	15.1471i	0.237596	+	0.501297i
$914$	−22.0043			−0.727838
$915$		0			0
$916$	4.69469	+	14.4488i	0.155117	+	0.477401i
$917$	25.7015	−	79.1011i	0.848738	−	2.61215i
$918$		0			0
$919$	43.7416	+	31.7801i	1.44290	+	1.04833i	0.987426	+	0.158083i	$0.0505313\pi$
$919$	43.7416	+	31.7801i	1.44290	+	1.04833i	0.455477	+	0.890248i	$0.349469\pi$
$920$	−1.33780	+	4.11731i	−0.0441058	+	0.135744i
$921$		0			0
$922$	12.0906	−	8.78433i	0.398182	−	0.289296i
$923$	−24.1992			−0.796528
$924$		0			0
$925$	−22.2553			−0.731749
$926$	−0.165442	+	0.120201i	−0.00543676	+	0.00395004i
$927$		0			0
$928$	8.85041	−	27.2388i	0.290529	−	0.894156i
$929$	−0.148122	−	0.107617i	−0.00485971	−	0.00353079i	0.585353	−	0.810779i	$-0.300956\pi$
$929$	−0.148122	−	0.107617i	−0.00485971	−	0.00353079i	−0.590212	+	0.807248i	$0.700956\pi$
$930$		0			0
$931$	11.6621	−	35.8921i	0.382208	−	1.17632i
$932$	−0.117614	−	0.361979i	−0.00385257	−	0.0118570i
$933$		0			0
$934$	6.47213			0.211775
$935$	−0.246345	+	1.31117i	−0.00805634	+	0.0428797i
$936$		0			0
$937$	−1.12949	+	0.820624i	−0.0368989	+	0.0268086i	−0.606082	−	0.795402i	$-0.707260\pi$
$937$	−1.12949	+	0.820624i	−0.0368989	+	0.0268086i	0.569183	+	0.822211i	$0.307260\pi$
$938$	−4.33546	−	13.3432i	−0.141558	−	0.435670i
$939$		0			0
$940$	0.597590	+	0.434175i	0.0194912	+	0.0141612i
$941$	−13.2972	−	9.66102i	−0.433478	−	0.314940i	0.349560	−	0.936914i	$-0.386331\pi$
$941$	−13.2972	−	9.66102i	−0.433478	−	0.314940i	−0.783038	+	0.621974i	$0.786331\pi$
$942$		0			0
$943$	8.93054	+	27.4854i	0.290818	+	0.895047i
$944$	13.7546	−	9.99332i	0.447675	−	0.325255i
$945$		0			0
$946$	−31.7308	+	4.09813i	−1.03166	+	0.133242i
$947$	−18.6801			−0.607022			−0.303511	−	0.952828i	$-0.598159\pi$
$947$	−18.6801			−0.607022			−0.303511	+	0.952828i	$0.598159\pi$
$948$		0			0
$949$	−1.93469	−	5.95437i	−0.0628028	−	0.193287i
$950$	−6.07565	+	18.6989i	−0.197120	+	0.606673i
$951$		0			0
$952$	−14.4381	−	10.4899i	−0.467941	−	0.339979i
$953$	−0.637622	+	1.96240i	−0.0206546	+	0.0635683i	−0.960853	−	0.277060i	$-0.910640\pi$
$953$	−0.637622	+	1.96240i	−0.0206546	+	0.0635683i	0.940198	+	0.340629i	$0.110640\pi$
$954$		0			0
$955$	3.70033	−	2.68845i	0.119740	−	0.0869961i
$956$	12.0406			0.389422
$957$		0			0
$958$	29.2703			0.945680
$959$	69.8275	−	50.7327i	2.25485	−	1.63824i
$960$		0			0
$961$	−1.43675	+	4.42187i	−0.0463469	+	0.142641i
$962$	16.8757	+	12.2609i	0.544093	+	0.395307i
$963$		0			0
$964$	0.418315	−	1.28744i	0.0134730	−	0.0414657i
$965$	−1.29308	−	3.97969i	−0.0416257	−	0.128111i
$966$		0			0
$967$	−0.772328			−0.0248364			−0.0124182	−	0.999923i	$-0.503953\pi$
$967$	−0.772328			−0.0248364			−0.0124182	+	0.999923i	$0.503953\pi$
$968$	21.3509	−	26.1028i	0.686244	−	0.838975i
$969$		0			0
$970$	−1.14115	+	0.829097i	−0.0366402	+	0.0266207i
$971$	−9.93662	−	30.5818i	−0.318881	−	0.981415i	−0.974127	−	0.226000i	$-0.927435\pi$
$971$	−9.93662	−	30.5818i	−0.318881	−	0.981415i	0.655246	−	0.755415i	$-0.272565\pi$
$972$		0			0
$973$	−42.8145	−	31.1065i	−1.37257	−	0.997230i
$974$	38.5527	+	28.0101i	1.23531	+	0.897503i
$975$		0			0
$976$	9.67506	+	29.7768i	0.309691	+	0.953132i
$977$	−22.0894	+	16.0489i	−0.706703	+	0.513450i	−0.882108	−	0.471047i	$-0.843876\pi$
$977$	−22.0894	+	16.0489i	−0.706703	+	0.513450i	0.175405	+	0.984496i	$0.443876\pi$
$978$		0			0
$979$	47.5114	+	25.9480i	1.51847	+	0.829301i
$980$	−1.77090			−0.0565694
$981$		0			0
$982$	−6.55765	−	20.1824i	−0.209263	−	0.644045i
$983$	1.74921	−	5.38352i	0.0557911	−	0.171707i	−0.919278	−	0.393609i	$-0.871226\pi$
$983$	1.74921	−	5.38352i	0.0557911	−	0.171707i	0.975069	+	0.221902i	$0.0712264\pi$
$984$		0			0
$985$	1.23502	+	0.897297i	0.0393511	+	0.0285903i
$986$	−5.10158	+	15.7010i	−0.162467	+	0.500023i
$987$		0			0
$988$	−5.23678	+	3.80475i	−0.166604	+	0.121045i
$989$	−37.7053			−1.19896
$990$		0			0
$991$	−31.1742			−0.990280			−0.495140	−	0.868813i	$-0.664883\pi$
$991$	−31.1742			−0.990280			−0.495140	+	0.868813i	$0.664883\pi$
$992$	−11.8726	+	8.62593i	−0.376955	+	0.273873i
$993$		0			0
$994$	10.3323	−	31.7997i	0.327722	−	1.00863i
$995$	3.83345	+	2.78517i	0.121529	+	0.0882957i
$996$		0			0
$997$	−12.7499	+	39.2400i	−0.403792	+	1.24274i	0.518108	+	0.855315i	$0.326637\pi$
$997$	−12.7499	+	39.2400i	−0.403792	+	1.24274i	−0.921900	+	0.387429i	$0.873363\pi$
$998$	2.69938	+	8.30785i	0.0854475	+	0.262980i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.a.190.2	yes	16
3.2	odd	2		297.2.f.d.190.3	yes	16
9.2	odd	6		891.2.n.f.190.2		32
9.4	even	3		891.2.n.i.784.2		32
9.5	odd	6		891.2.n.f.784.3		32
9.7	even	3		891.2.n.i.190.3		32
11.2	odd	10		3267.2.a.bf.1.4		8
11.4	even	5	inner	297.2.f.a.136.2	✓	16
11.9	even	5		3267.2.a.bm.1.5		8
33.2	even	10		3267.2.a.bl.1.5		8
33.20	odd	10		3267.2.a.be.1.4		8
33.26	odd	10		297.2.f.d.136.3	yes	16
99.4	even	15		891.2.n.i.136.3		32
99.59	odd	30		891.2.n.f.136.2		32
99.70	even	15		891.2.n.i.433.2		32
99.92	odd	30		891.2.n.f.433.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.a.136.2	✓	16	11.4	even	5	inner
297.2.f.a.190.2	yes	16	1.1	even	1	trivial
297.2.f.d.136.3	yes	16	33.26	odd	10
297.2.f.d.190.3	yes	16	3.2	odd	2
891.2.n.f.136.2		32	99.59	odd	30
891.2.n.f.190.2		32	9.2	odd	6
891.2.n.f.433.3		32	99.92	odd	30
891.2.n.f.784.3		32	9.5	odd	6
891.2.n.i.136.3		32	99.4	even	15
891.2.n.i.190.3		32	9.7	even	3
891.2.n.i.433.2		32	99.70	even	15
891.2.n.i.784.2		32	9.4	even	3
3267.2.a.be.1.4		8	33.20	odd	10
3267.2.a.bf.1.4		8	11.2	odd	10
3267.2.a.bl.1.5		8	33.2	even	10
3267.2.a.bm.1.5		8	11.9	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)

\(f(q)\)	\(=\)	\(q+(-0.984246 + 0.715096i) q^{2} +(-0.160657 + 0.494452i) q^{4} +(-0.240251 - 0.174552i) q^{5} +(1.32806 - 4.08735i) q^{7} +(-0.947351 - 2.91565i) q^{8} +O(q^{10})\)	\(q+(-0.984246 + 0.715096i) q^{2} +(-0.160657 + 0.494452i) q^{4} +(-0.240251 - 0.174552i) q^{5} +(1.32806 - 4.08735i) q^{7} +(-0.947351 - 2.91565i) q^{8} +0.361288 q^{10} +(-2.91081 - 1.58971i) q^{11} +(3.06143 - 2.22426i) q^{13} +(1.61571 + 4.97265i) q^{14} +(2.17618 + 1.58109i) q^{16} +(1.09583 + 0.796170i) q^{17} +(1.01673 + 3.12917i) q^{19} +(0.124906 - 0.0907493i) q^{20} +(4.00175 - 0.516838i) q^{22} +4.75523 q^{23} +(-1.51783 - 4.67141i) q^{25} +(-1.42264 + 4.37843i) q^{26} +(1.80763 + 1.31332i) q^{28} +(3.09579 - 9.52785i) q^{29} +(-4.15291 + 3.01727i) q^{31} +2.85886 q^{32} -1.64791 q^{34} +(-1.03252 + 0.750173i) q^{35} +(1.40015 - 4.30921i) q^{37} +(-3.23837 - 2.35281i) q^{38} +(-0.281331 + 0.865849i) q^{40} +(1.87805 + 5.78003i) q^{41} -7.92922 q^{43} +(1.25368 - 1.18386i) q^{44} +(-4.68032 + 3.40045i) q^{46} +(1.47844 + 4.55017i) q^{47} +(-9.27956 - 6.74199i) q^{49} +(4.83443 + 3.51242i) q^{50} +(0.607948 + 1.87107i) q^{52} +(1.16402 - 0.845714i) q^{53} +(0.421835 + 0.890019i) q^{55} -13.1754 q^{56} +(3.76632 + 11.5915i) q^{58} +(1.95315 - 6.01118i) q^{59} +(9.41653 + 6.84151i) q^{61} +(1.92985 - 5.93946i) q^{62} +(-7.16618 + 5.20654i) q^{64} -1.12376 q^{65} -2.68331 q^{67} +(-0.569722 + 0.413927i) q^{68} +(0.479812 - 1.47671i) q^{70} +(-5.17360 - 3.75884i) q^{71} +(0.511265 - 1.57351i) q^{73} +(1.70341 + 5.24256i) q^{74} -1.71057 q^{76} +(-10.3634 + 9.78625i) q^{77} +(-5.52312 + 4.01278i) q^{79} +(-0.246847 - 0.759716i) q^{80} +(-5.98174 - 4.34599i) q^{82} +(-4.08880 - 2.97069i) q^{83} +(-0.124302 - 0.382561i) q^{85} +(7.80430 - 5.67016i) q^{86} +(-1.87749 + 9.99291i) q^{88} -16.3224 q^{89} +(-5.02556 - 15.4671i) q^{91} +(-0.763962 + 2.35123i) q^{92} +(-4.70896 - 3.42126i) q^{94} +(0.301934 - 0.929258i) q^{95} +(-3.15857 + 2.29484i) q^{97} +13.9545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - q^{5} - 2 q^{7}+O(q^{10}) \) 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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