LMFDB - Embedded newform 720.2.z.g.667.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.6
Root			$1.41323 + 0.0526497i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.516777 + 1.31641i) q^{2} +(-1.46588 + 1.36058i) q^{4} +(-2.07160 + 0.841703i) q^{5} +(-1.13975 - 1.13975i) q^{7} +(-2.54862 - 1.22659i) q^{8} +O(q^{10})$	\(q+(0.516777 + 1.31641i) q^{2} +(-1.46588 + 1.36058i) q^{4} +(-2.07160 + 0.841703i) q^{5} +(-1.13975 - 1.13975i) q^{7} +(-2.54862 - 1.22659i) q^{8} +(-2.17858 - 2.29211i) q^{10} +(2.32204 - 2.32204i) q^{11} -1.36502i q^{13} +(0.911384 - 2.08938i) q^{14} +(0.297625 - 3.98891i) q^{16} +(-5.25380 - 5.25380i) q^{17} +(-3.69752 + 3.69752i) q^{19} +(1.89152 - 4.05243i) q^{20} +(4.25673 + 1.85678i) q^{22} +(0.911118 - 0.911118i) q^{23} +(3.58307 - 3.48735i) q^{25} +(1.79693 - 0.705412i) q^{26} +(3.22146 + 0.120015i) q^{28} +(2.37343 + 2.37343i) q^{29} +0.242577i q^{31} +(5.40486 - 1.66958i) q^{32} +(4.20112 - 9.63121i) q^{34} +(3.32044 + 1.40178i) q^{35} -3.34494i q^{37} +(-6.77825 - 2.95666i) q^{38} +(6.31216 + 0.395820i) q^{40} -2.66956i q^{41} -9.04874i q^{43} +(-0.244509 + 6.56316i) q^{44} +(1.67025 + 0.728562i) q^{46} +(-7.87820 + 7.87820i) q^{47} -4.40194i q^{49} +(6.44244 + 2.91462i) q^{50} +(1.85723 + 2.00096i) q^{52} +5.80113 q^{53} +(-2.85587 + 6.76480i) q^{55} +(1.50679 + 4.30279i) q^{56} +(-1.89788 + 4.35095i) q^{58} +(-5.91474 - 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(-0.319332 + 0.125358i) q^{62} +(4.99096 + 6.25222i) q^{64} +(1.14894 + 2.82778i) q^{65} -4.54673i q^{67} +(14.8497 + 0.553222i) q^{68} +(-0.129391 + 5.09547i) q^{70} -15.4389 q^{71} +(-1.49307 - 1.49307i) q^{73} +(4.40332 - 1.72859i) q^{74} +(0.389347 - 10.4509i) q^{76} -5.29308 q^{77} -10.3024 q^{79} +(2.74092 + 8.51395i) q^{80} +(3.51424 - 1.37957i) q^{82} -3.26589 q^{83} +(15.3059 + 6.46165i) q^{85} +(11.9119 - 4.67618i) q^{86} +(-8.76618 + 3.06981i) q^{88} -9.77206 q^{89} +(-1.55578 + 1.55578i) q^{91} +(-0.0959403 + 2.57524i) q^{92} +(-14.4422 - 6.29969i) q^{94} +(4.54758 - 10.7720i) q^{95} +(-1.63587 - 1.63587i) q^{97} +(5.79477 - 2.27482i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.516777	+	1.31641i	0.365417	+	0.930844i
$2$	0.516777	+	1.31641i	0.365417	+	0.930844i
$3$		0			0
$3$		0			0
$4$	−1.46588	+	1.36058i	−0.732941	+	0.680292i
$5$	−2.07160	+	0.841703i	−0.926449	+	0.376421i
$5$	−2.07160	+	0.841703i	−0.926449	+	0.376421i
$6$		0			0
$7$	−1.13975	−	1.13975i	−0.430785	−	0.430785i	0.458111	−	0.888895i	$-0.348526\pi$
$7$	−1.13975	−	1.13975i	−0.430785	−	0.430785i	−0.888895	+	0.458111i	$0.848526\pi$
$8$	−2.54862	−	1.22659i	−0.901074	−	0.433664i
$9$		0			0
$10$	−2.17858	−	2.29211i	−0.688929	−	0.724829i
$11$	2.32204	−	2.32204i	0.700120	−	0.700120i	−0.264316	−	0.964436i	$-0.585146\pi$
$11$	2.32204	−	2.32204i	0.700120	−	0.700120i	0.964436	+	0.264316i	$0.0851462\pi$
$12$		0			0
$13$		−	1.36502i		−	0.378589i	−0.981920	−	0.189294i	$-0.939380\pi$
$13$		−	1.36502i		−	0.378589i	0.981920	−	0.189294i	$-0.0606201\pi$
$14$	0.911384	−	2.08938i	0.243578	−	0.558409i
$15$		0			0
$16$	0.297625	−	3.98891i	0.0744064	−	0.997228i
$17$	−5.25380	−	5.25380i	−1.27423	−	1.27423i	−0.943845	−	0.330389i	$-0.892820\pi$
$17$	−5.25380	−	5.25380i	−1.27423	−	1.27423i	−0.330389	−	0.943845i	$-0.607180\pi$
$18$		0			0
$19$	−3.69752	+	3.69752i	−0.848269	+	0.848269i	−0.989917	−	0.141648i	$-0.954760\pi$
$19$	−3.69752	+	3.69752i	−0.848269	+	0.848269i	0.141648	+	0.989917i	$0.454760\pi$
$20$	1.89152	−	4.05243i	0.422957	−	0.906150i
$21$		0			0
$22$	4.25673	+	1.85678i	0.907538	+	0.395867i
$23$	0.911118	−	0.911118i	0.189981	−	0.189981i	−0.605707	−	0.795688i	$-0.707110\pi$
$23$	0.911118	−	0.911118i	0.189981	−	0.189981i	0.795688	+	0.605707i	$0.207110\pi$
$24$		0			0
$25$	3.58307	−	3.48735i	0.716615	−	0.697469i
$26$	1.79693	−	0.705412i	0.352407	−	0.138343i
$27$		0			0
$28$	3.22146	+	0.120015i	0.608799	+	0.0226807i
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	0.892259	−	0.451524i	$-0.149119\pi$
$29$	2.37343	+	2.37343i	0.440736	+	0.440736i	−0.451524	+	0.892259i	$0.649119\pi$
$30$		0			0
$31$			0.242577i			0.0435681i	0.999763	+	0.0217841i	$0.00693463\pi$
$31$			0.242577i			0.0435681i	−0.999763	+	0.0217841i	$0.993065\pi$
$32$	5.40486	−	1.66958i	0.955453	−	0.295143i
$33$		0			0
$34$	4.20112	−	9.63121i	0.720487	−	1.65174i
$35$	3.32044	+	1.40178i	0.561256	+	0.236944i
$36$		0			0
$37$		−	3.34494i		−	0.549905i	−0.961458	−	0.274953i	$-0.911338\pi$
$37$		−	3.34494i		−	0.549905i	0.961458	−	0.274953i	$-0.0886621\pi$
$38$	−6.77825	−	2.95666i	−1.09958	−	0.479634i
$39$		0			0
$40$	6.31216	+	0.395820i	0.998040	+	0.0625846i
$41$		−	2.66956i		−	0.416915i	−0.978031	−	0.208457i	$-0.933156\pi$
$41$		−	2.66956i		−	0.416915i	0.978031	−	0.208457i	$-0.0668442\pi$
$42$		0			0
$43$		−	9.04874i		−	1.37992i	−0.723847	−	0.689960i	$-0.757628\pi$
$43$		−	9.04874i		−	1.37992i	0.723847	−	0.689960i	$-0.242372\pi$
$44$	−0.244509	+	6.56316i	−0.0368611	+	0.989433i
$45$		0			0
$46$	1.67025	+	0.728562i	0.246265	+	0.107421i
$47$	−7.87820	+	7.87820i	−1.14915	+	1.14915i	−0.162435	+	0.986719i	$0.551935\pi$
$47$	−7.87820	+	7.87820i	−1.14915	+	1.14915i	−0.986719	+	0.162435i	$0.948065\pi$
$48$		0			0
$49$		−	4.40194i		−	0.628849i
$50$	6.44244	+	2.91462i	0.911098	+	0.412190i
$51$		0			0
$52$	1.85723	+	2.00096i	0.257551	+	0.277483i
$53$	5.80113			0.796846			0.398423	−	0.917202i	$-0.369558\pi$
$53$	5.80113			0.796846			0.398423	+	0.917202i	$0.369558\pi$
$54$		0			0
$55$	−2.85587	+	6.76480i	−0.385086	+	0.912165i
$56$	1.50679	+	4.30279i	0.201353	+	0.574985i
$57$		0			0
$58$	−1.89788	+	4.35095i	−0.249204	+	0.571308i
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	0.208079	−	0.978112i	$-0.433279\pi$
$59$	−5.91474	−	5.91474i	−0.770033	−	0.770033i	−0.978112	+	0.208079i	$0.933279\pi$
$60$		0			0
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	−0.990686	−	0.136163i	$-0.956523\pi$
$61$	−6.67404	+	6.67404i	−0.854523	+	0.854523i	0.136163	+	0.990686i	$0.456523\pi$
$62$	−0.319332	+	0.125358i	−0.0405551	+	0.0159205i
$63$		0			0
$64$	4.99096	+	6.25222i	0.623870	+	0.781528i
$65$	1.14894	+	2.82778i	0.142509	+	0.350743i
$66$		0			0
$67$		−	4.54673i		−	0.555471i	−0.960658	−	0.277736i	$-0.910416\pi$
$67$		−	4.54673i		−	0.555471i	0.960658	−	0.277736i	$-0.0895839\pi$
$68$	14.8497	+	0.553222i	1.80079	+	0.0670881i
$69$		0			0
$70$	−0.129391	+	5.09547i	−0.0154652	+	0.609025i
$71$	−15.4389			−1.83226			−0.916128	−	0.400885i	$-0.868703\pi$
$71$	−15.4389			−1.83226			−0.916128	+	0.400885i	$0.868703\pi$
$72$		0			0
$73$	−1.49307	−	1.49307i	−0.174750	−	0.174750i	0.614313	−	0.789063i	$-0.289433\pi$
$73$	−1.49307	−	1.49307i	−0.174750	−	0.174750i	−0.789063	+	0.614313i	$0.789433\pi$
$74$	4.40332	−	1.72859i	0.511876	−	0.200944i
$75$		0			0
$76$	0.389347	−	10.4509i	0.0446611	−	1.19880i
$77$	−5.29308			−0.603202
$78$		0			0
$79$	−10.3024			−1.15911			−0.579556	−	0.814932i	$-0.696774\pi$
$79$	−10.3024			−1.15911			−0.579556	+	0.814932i	$0.696774\pi$
$80$	2.74092	+	8.51395i	0.306444	+	0.951889i
$81$		0			0
$82$	3.51424	−	1.37957i	0.388083	−	0.152348i
$83$	−3.26589			−0.358478			−0.179239	−	0.983806i	$-0.557364\pi$
$83$	−3.26589			−0.358478			−0.179239	+	0.983806i	$0.557364\pi$
$84$		0			0
$85$	15.3059	+	6.46165i	1.66016	+	0.700864i
$86$	11.9119	−	4.67618i	1.28449	−	0.504246i
$87$		0			0
$88$	−8.76618	+	3.06981i	−0.934477	+	0.327243i
$89$	−9.77206			−1.03584			−0.517918	−	0.855430i	$-0.673293\pi$
$89$	−9.77206			−1.03584			−0.517918	+	0.855430i	$0.673293\pi$
$90$		0			0
$91$	−1.55578	+	1.55578i	−0.163090	+	0.163090i
$92$	−0.0959403	+	2.57524i	−0.0100025	+	0.268488i
$93$		0			0
$94$	−14.4422	−	6.29969i	−1.48960	−	0.649763i
$95$	4.54758	−	10.7720i	0.466571	−	1.10518i
$96$		0			0
$97$	−1.63587	−	1.63587i	−0.166097	−	0.166097i	0.619164	−	0.785262i	$-0.287472\pi$
$97$	−1.63587	−	1.63587i	−0.166097	−	0.166097i	−0.785262	+	0.619164i	$0.787472\pi$
$98$	5.79477	−	2.27482i	0.585360	−	0.229792i
$99$		0			0
$100$	−0.507540	+	9.98711i	−0.0507540	+	0.998711i
$101$	6.63953	+	6.63953i	0.660658	+	0.660658i	0.955535	−	0.294877i	$-0.0952787\pi$
$101$	6.63953	+	6.63953i	0.660658	+	0.660658i	−0.294877	+	0.955535i	$0.595279\pi$
$102$		0			0
$103$	1.62219	−	1.62219i	0.159839	−	0.159839i	−0.622656	−	0.782496i	$-0.713946\pi$
$103$	1.62219	−	1.62219i	0.159839	−	0.159839i	0.782496	+	0.622656i	$0.213946\pi$
$104$	−1.67432	+	3.47893i	−0.164180	+	0.341137i
$105$		0			0
$106$	2.99789	+	7.63667i	0.291181	+	0.741739i
$107$	−3.65206			−0.353058			−0.176529	−	0.984295i	$-0.556487\pi$
$107$	−3.65206			−0.353058			−0.176529	+	0.984295i	$0.556487\pi$
$108$		0			0
$109$	5.20757	+	5.20757i	0.498795	+	0.498795i	0.911063	−	0.412268i	$-0.135263\pi$
$109$	5.20757	+	5.20757i	0.498795	+	0.498795i	−0.412268	+	0.911063i	$0.635263\pi$
$110$	−10.3811	−	0.263611i	−0.989800	−	0.0251344i
$111$		0			0
$112$	−4.88558	+	4.20714i	−0.461644	+	0.397537i
$113$	4.27905	−	4.27905i	0.402539	−	0.402539i	−0.476588	−	0.879127i	$-0.658127\pi$
$113$	4.27905	−	4.27905i	0.402539	−	0.402539i	0.879127	+	0.476588i	$0.158127\pi$
$114$		0			0
$115$	−1.12058	+	2.65437i	−0.104495	+	0.247521i
$116$	−6.70843	−	0.249921i	−0.622862	−	0.0232046i
$117$		0			0
$118$	4.72963	−	10.8428i	0.435398	−	0.998164i
$119$			11.9760i			1.09784i
$120$		0			0
$121$			0.216302i			0.0196639i
$122$	−12.2348	−	5.33680i	−1.10768	−	0.483171i
$123$		0			0
$124$	−0.330046	−	0.355590i	−0.0296390	−	0.0319329i
$125$	−4.48739	+	10.2403i	−0.401365	+	0.915918i
$126$		0			0
$127$	−7.29257	+	7.29257i	−0.647111	+	0.647111i	−0.952294	−	0.305183i	$-0.901282\pi$
$127$	−7.29257	+	7.29257i	−0.647111	+	0.647111i	0.305183	+	0.952294i	$0.401282\pi$
$128$	−5.65129	+	9.80117i	−0.499508	+	0.866309i
$129$		0			0
$130$	−3.12878	+	2.97381i	−0.274412	+	0.260821i
$131$	11.9793	+	11.9793i	1.04664	+	1.04664i	0.998858	+	0.0477778i	$0.0152139\pi$
$131$	11.9793	+	11.9793i	1.04664	+	1.04664i	0.0477778	+	0.998858i	$0.484786\pi$
$132$		0			0
$133$	8.42848			0.730842
$134$	5.98537	−	2.34965i	0.517057	−	0.202978i
$135$		0			0
$136$	6.94571	+	19.8342i	0.595590	+	1.70077i
$137$	4.92762	−	4.92762i	0.420995	−	0.420995i	−0.464551	−	0.885546i	$-0.653784\pi$
$137$	4.92762	−	4.92762i	0.420995	−	0.420995i	0.885546	+	0.464551i	$0.153784\pi$
$138$		0			0
$139$	10.3015	+	10.3015i	0.873761	+	0.873761i	0.992880	−	0.119119i	$-0.0380071\pi$
$139$	10.3015	+	10.3015i	0.873761	+	0.873761i	−0.119119	+	0.992880i	$0.538007\pi$
$140$	−6.77461	+	2.46289i	−0.572559	+	0.208152i
$141$		0			0
$142$	−7.97845	−	20.3239i	−0.669537	−	1.70555i
$143$	−3.16963	−	3.16963i	−0.265058	−	0.265058i
$144$		0			0
$145$	−6.91454	−	2.91909i	−0.574221	−	0.242417i
$146$	1.19391	−	2.73707i	0.0988086	−	0.226522i
$147$		0			0
$148$	4.55107	+	4.90329i	0.374096	+	0.403048i
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.287896	−	0.957662i	$-0.407044\pi$
$149$	15.2040	−	15.2040i	1.24556	−	1.24556i	0.957662	−	0.287896i	$-0.0929557\pi$
$150$		0			0
$151$	−10.7055			−0.871204			−0.435602	−	0.900139i	$-0.643464\pi$
$151$	−10.7055			−0.871204			−0.435602	+	0.900139i	$0.643464\pi$
$152$	13.9589	−	4.88825i	1.13222	−	0.396489i
$153$		0			0
$154$	−2.73534	−	6.96787i	−0.220420	−	0.561487i
$155$	−0.204178	−	0.502523i	−0.0164000	−	0.0403636i
$156$		0			0
$157$	2.34588			0.187222			0.0936108	−	0.995609i	$-0.470159\pi$
$157$	2.34588			0.187222			0.0936108	+	0.995609i	$0.470159\pi$
$158$	−5.32405	−	13.5622i	−0.423559	−	1.07895i
$159$		0			0
$160$	−9.79143	+	8.00799i	−0.774080	+	0.633087i
$161$	−2.07689			−0.163682
$162$		0			0
$163$	−2.73625			−0.214319			−0.107160	−	0.994242i	$-0.534176\pi$
$163$	−2.73625			−0.214319			−0.107160	+	0.994242i	$0.534176\pi$
$164$	3.63215	+	3.91326i	0.283624	+	0.305574i
$165$		0			0
$166$	−1.68774	−	4.29926i	−0.130994	−	0.333687i
$167$	−10.1328	−	10.1328i	−0.784097	−	0.784097i	0.196423	−	0.980519i	$-0.437068\pi$
$167$	−10.1328	−	10.1328i	−0.784097	−	0.784097i	−0.980519	+	0.196423i	$0.937068\pi$
$168$		0			0
$169$	11.1367			0.856670
$170$	−0.596443	+	23.4881i	−0.0457451	+	1.80146i
$171$		0			0
$172$	12.3116	+	13.2644i	0.938748	+	1.01140i
$173$		−	8.79590i		−	0.668740i	−0.942442	−	0.334370i	$-0.891477\pi$
$173$		−	8.79590i		−	0.668740i	0.942442	−	0.334370i	$-0.108523\pi$
$174$		0			0
$175$	−8.05851	−	0.109105i	−0.609166	−	0.00824753i
$176$	−8.57130	−	9.95349i	−0.646086	−	0.750273i
$177$		0			0
$178$	−5.04998	−	12.8641i	−0.378512	−	0.964202i
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	−0.909832	−	0.414977i	$-0.863790\pi$
$179$	−6.62071	+	6.62071i	−0.494855	+	0.494855i	0.414977	+	0.909832i	$0.363790\pi$
$180$		0			0
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	0.455765	−	0.890100i	$-0.349366\pi$
$181$	−5.84339	−	5.84339i	−0.434336	−	0.434336i	−0.890100	+	0.455765i	$0.849366\pi$
$182$	−2.85204	−	1.24406i	−0.211408	−	0.0922157i
$183$		0			0
$184$	−3.43966	+	1.20453i	−0.253575	+	0.0887992i
$185$	2.81545	+	6.92939i	0.206996	+	0.509459i
$186$		0			0
$187$	−24.3990			−1.78423
$188$	0.829571	−	22.2675i	0.0605027	−	1.62402i
$189$		0			0
$190$	16.5305	+	0.419764i	1.19925	+	0.0304529i
$191$		−	1.83906i		−	0.133070i	−0.997784	−	0.0665349i	$-0.978806\pi$
$191$		−	1.83906i		−	0.133070i	0.997784	−	0.0665349i	$-0.0211944\pi$
$192$		0			0
$193$	6.18343	−	6.18343i	0.445093	−	0.445093i	−0.448626	−	0.893719i	$-0.648087\pi$
$193$	6.18343	−	6.18343i	0.445093	−	0.445093i	0.893719	+	0.448626i	$0.148087\pi$
$194$	1.30810	−	2.99886i	0.0939160	−	0.215305i
$195$		0			0
$196$	5.98921	+	6.45273i	0.427801	+	0.460910i
$197$		−	5.55669i		−	0.395898i	−0.980212	−	0.197949i	$-0.936572\pi$
$197$		−	5.55669i		−	0.395898i	0.980212	−	0.197949i	$-0.0634280\pi$
$198$		0			0
$199$			6.96413i			0.493674i	0.969057	+	0.246837i	$0.0793912\pi$
$199$			6.96413i			0.493674i	−0.969057	+	0.246837i	$0.920609\pi$
$200$	−13.4094	+	4.49298i	−0.948191	+	0.317702i
$201$		0			0
$202$	−5.30920	+	12.1715i	−0.373554	+	0.856385i
$203$		−	5.41024i		−	0.379724i
$204$		0			0
$205$	2.24697	+	5.53026i	0.156935	+	0.386250i
$206$	2.97379	+	1.29716i	0.207194	+	0.0903776i
$207$		0			0
$208$	−5.44495	−	0.406265i	−0.377539	−	0.0281694i
$209$			17.1715i			1.18778i
$210$		0			0
$211$	5.43389	+	5.43389i	0.374084	+	0.374084i	0.868962	−	0.494878i	$-0.164787\pi$
$211$	5.43389	+	5.43389i	0.374084	+	0.374084i	−0.494878	+	0.868962i	$0.664787\pi$
$212$	−8.50377	+	7.89291i	−0.584041	+	0.542088i
$213$		0			0
$214$	−1.88730	−	4.80761i	−0.129013	−	0.328642i
$215$	7.61635	+	18.7454i	0.519431	+	1.27843i
$216$		0			0
$217$	0.276477	−	0.276477i	0.0187685	−	0.0187685i
$218$	−4.16416	+	9.54647i	−0.282032	+	0.646568i
$219$		0			0
$220$	−5.01770	−	13.8021i	−0.338293	−	0.930534i
$221$	−7.17155	+	7.17155i	−0.482411	+	0.482411i
$222$		0			0
$223$	8.61776	+	8.61776i	0.577088	+	0.577088i	0.934100	−	0.357012i	$-0.116204\pi$
$223$	8.61776	+	8.61776i	0.577088	+	0.577088i	−0.357012	+	0.934100i	$0.616204\pi$
$224$	−8.06309	−	4.25728i	−0.538738	−	0.284452i
$225$		0			0
$226$	7.84431	+	3.42168i	0.521796	+	0.227607i
$227$		−	6.01977i		−	0.399546i	−0.979842	−	0.199773i	$-0.935980\pi$
$227$		−	6.01977i		−	0.399546i	0.979842	−	0.199773i	$-0.0640205\pi$
$228$		0			0
$229$	−0.568504	+	0.568504i	−0.0375678	+	0.0375678i	−0.725641	−	0.688073i	$-0.758457\pi$
$229$	−0.568504	+	0.568504i	−0.0375678	+	0.0375678i	0.688073	+	0.725641i	$0.258457\pi$
$230$	−4.07333	−	0.103436i	−0.268588	−	0.00682034i
$231$		0			0
$232$	−3.13776	−	8.96022i	−0.206004	−	0.588267i
$233$	−12.6979	−	12.6979i	−0.831869	−	0.831869i	0.155904	−	0.987772i	$-0.450171\pi$
$233$	−12.6979	−	12.6979i	−0.831869	−	0.831869i	−0.987772	+	0.155904i	$0.950171\pi$
$234$		0			0
$235$	9.68940	−	22.9516i	0.632067	−	1.49720i
$236$	16.7178	+	0.622819i	1.08824	+	0.0405421i
$237$		0			0
$238$	−15.7654	+	6.18894i	−1.02192	+	0.401169i
$239$	−1.78306			−0.115336			−0.0576682	−	0.998336i	$-0.518367\pi$
$239$	−1.78306			−0.115336			−0.0576682	+	0.998336i	$0.518367\pi$
$240$		0			0
$241$	10.4440			0.672754			0.336377	−	0.941727i	$-0.390798\pi$
$241$	10.4440			0.672754			0.336377	+	0.941727i	$0.390798\pi$
$242$	−0.284743	+	0.111780i	−0.0183040	+	0.00718550i
$243$		0			0
$244$	0.702773	−	18.8639i	0.0449904	−	1.20764i
$245$	3.70513	+	9.11908i	0.236712	+	0.582596i
$246$		0			0
$247$	5.04719	+	5.04719i	0.321145	+	0.321145i
$248$	0.297542	−	0.618238i	0.0188939	−	0.0392581i
$249$		0			0
$250$	−15.7994	−	0.615321i	−0.999242	−	0.0389163i
$251$	12.6497	−	12.6497i	0.798445	−	0.798445i	−0.184406	−	0.982850i	$-0.559036\pi$
$251$	12.6497	−	12.6497i	0.798445	−	0.798445i	0.982850	+	0.184406i	$0.0590360\pi$
$252$		0			0
$253$		−	4.23130i		−	0.266019i
$254$	−13.3687	−	5.83140i	−0.838825	−	0.365894i
$255$		0			0
$256$	−15.8228	−	2.37440i	−0.988927	−	0.148400i
$257$	4.13062	+	4.13062i	0.257661	+	0.257661i	0.824102	−	0.566441i	$-0.191680\pi$
$257$	4.13062	+	4.13062i	0.257661	+	0.257661i	−0.566441	+	0.824102i	$0.691680\pi$
$258$		0			0
$259$	−3.81240	+	3.81240i	−0.236891	+	0.236891i
$260$	−5.53165	−	2.58197i	−0.343058	−	0.160127i
$261$		0			0
$262$	−9.57907	+	21.9603i	−0.591797	+	1.35671i
$263$	−17.1303	+	17.1303i	−1.05630	+	1.05630i	−0.0579798	+	0.998318i	$0.518466\pi$
$263$	−17.1303	+	17.1303i	−1.05630	+	1.05630i	−0.998318	+	0.0579798i	$0.981534\pi$
$264$		0			0
$265$	−12.0176	+	4.88282i	−0.738237	+	0.299949i
$266$	4.35565	+	11.0954i	0.267062	+	0.680300i
$267$		0			0
$268$	6.18620	+	6.66497i	0.377883	+	0.407128i
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.971775	+	0.235910i	$0.0758070\pi$
$269$	19.8075	+	19.8075i	1.20768	+	1.20768i	0.235910	+	0.971775i	$0.424193\pi$
$270$		0			0
$271$		−	27.9542i		−	1.69810i	−0.528316	−	0.849048i	$-0.677176\pi$
$271$		−	27.9542i		−	1.69810i	0.528316	−	0.849048i	$-0.322824\pi$
$272$	−22.5206	+	19.3933i	−1.36551	+	1.17589i
$273$		0			0
$274$	9.03326	+	3.94030i	0.545719	+	0.238042i
$275$	0.222281	−	16.4178i	0.0134041	−	0.990029i
$276$		0			0
$277$		−	26.0257i		−	1.56373i	−0.623447	−	0.781866i	$-0.714268\pi$
$277$		−	26.0257i		−	1.56373i	0.623447	−	0.781866i	$-0.285732\pi$
$278$	−8.23743	+	18.8846i	−0.494048	+	1.13262i
$279$		0			0
$280$	−6.74314	−	7.64541i	−0.402980	−	0.456901i
$281$		−	24.1001i		−	1.43769i	−0.695170	−	0.718846i	$-0.744671\pi$
$281$		−	24.1001i		−	1.43769i	0.695170	−	0.718846i	$-0.255329\pi$
$282$		0			0
$283$		−	4.73708i		−	0.281590i	−0.990039	−	0.140795i	$-0.955034\pi$
$283$		−	4.73708i		−	0.281590i	0.990039	−	0.140795i	$-0.0449658\pi$
$284$	22.6316	−	21.0059i	1.34294	−	1.24647i
$285$		0			0
$286$	2.53455	−	5.81053i	0.149871	−	0.343584i
$287$	−3.04262	+	3.04262i	−0.179600	+	0.179600i
$288$		0			0
$289$			38.2049i			2.24734i
$290$	0.269446	−	10.6109i	0.0158224	−	0.623093i
$291$		0			0
$292$	4.22010	+	0.157219i	0.246963	+	0.00920056i
$293$	3.11001			0.181689			0.0908445	−	0.995865i	$-0.471043\pi$
$293$	3.11001			0.181689			0.0908445	+	0.995865i	$0.471043\pi$
$294$		0			0
$295$	17.2314	+	7.27454i	1.00325	+	0.423540i
$296$	−4.10287	+	8.52500i	−0.238474	+	0.495505i
$297$		0			0
$298$	27.8718	+	12.1576i	1.61457	+	0.704273i
$299$	−1.24370	−	1.24370i	−0.0719248	−	0.0719248i
$300$		0			0
$301$	−10.3133	+	10.3133i	−0.594449	+	0.594449i
$302$	−5.53238	−	14.0929i	−0.318352	−	0.810955i
$303$		0			0
$304$	13.6486	+	15.8495i	0.782801	+	0.909034i
$305$	8.20840	−	19.4435i	0.470012	−	1.11333i
$306$		0			0
$307$			14.5670i			0.831382i	0.909506	+	0.415691i	$0.136460\pi$
$307$			14.5670i			0.831382i	−0.909506	+	0.415691i	$0.863540\pi$
$308$	7.75903	−	7.20167i	0.442112	−	0.410353i
$309$		0			0
$310$	0.556014	−	0.528475i	0.0315794	−	0.0300153i
$311$	14.4572			0.819791			0.409896	−	0.912132i	$-0.365565\pi$
$311$	14.4572			0.819791			0.409896	+	0.912132i	$0.365565\pi$
$312$		0			0
$313$	−10.1273	−	10.1273i	−0.572429	−	0.572429i	0.360377	−	0.932807i	$-0.382648\pi$
$313$	−10.1273	−	10.1273i	−0.572429	−	0.572429i	−0.932807	+	0.360377i	$0.882648\pi$
$314$	1.21230	+	3.08815i	0.0684139	+	0.174274i
$315$		0			0
$316$	15.1021	−	14.0173i	0.849561	−	0.788534i
$317$	13.8750			0.779295			0.389648	−	0.920964i	$-0.372597\pi$
$317$	13.8750			0.779295			0.389648	+	0.920964i	$0.372597\pi$
$318$		0			0
$319$	11.0224			0.617136
$320$	−15.6018	−	8.75121i	−0.872167	−	0.489208i
$321$		0			0
$322$	−1.07329	−	2.73405i	−0.0598121	−	0.152362i
$323$	38.8520			2.16179
$324$		0			0
$325$	−4.76030	−	4.89097i	−0.264054	−	0.271302i
$326$	−1.41403	−	3.60203i	−0.0783158	−	0.199498i
$327$		0			0
$328$	−3.27445	+	6.80369i	−0.180801	+	0.375671i
$329$	17.9584			0.990076
$330$		0			0
$331$	1.69458	−	1.69458i	0.0931425	−	0.0931425i	−0.659000	−	0.752143i	$-0.729020\pi$
$331$	1.69458	−	1.69458i	0.0931425	−	0.0931425i	0.752143	+	0.659000i	$0.229020\pi$
$332$	4.78741	−	4.44352i	0.262743	−	0.243870i
$333$		0			0
$334$	8.10251	−	18.5753i	0.443350	−	1.01639i
$335$	3.82699	+	9.41902i	0.209091	+	0.514616i
$336$		0			0
$337$	−9.53338	−	9.53338i	−0.519316	−	0.519316i	0.398048	−	0.917364i	$-0.369688\pi$
$337$	−9.53338	−	9.53338i	−0.519316	−	0.519316i	−0.917364	+	0.398048i	$0.869688\pi$
$338$	5.75520	+	14.6605i	0.313042	+	0.797427i
$339$		0			0
$340$	−31.2283	+	11.3530i	−1.69359	+	0.615701i
$341$	0.563273	+	0.563273i	0.0305029	+	0.0305029i
$342$		0			0
$343$	−12.9954	+	12.9954i	−0.701683	+	0.701683i
$344$	−11.0991	+	23.0618i	−0.598422	+	1.24341i
$345$		0			0
$346$	11.5790	−	4.54552i	0.622492	−	0.244369i
$347$	6.67273			0.358211			0.179105	−	0.983830i	$-0.442680\pi$
$347$	6.67273			0.358211			0.179105	+	0.983830i	$0.442680\pi$
$348$		0			0
$349$	2.02618	+	2.02618i	0.108459	+	0.108459i	0.759254	−	0.650795i	$-0.225564\pi$
$349$	2.02618	+	2.02618i	0.108459	+	0.108459i	−0.650795	+	0.759254i	$0.725564\pi$
$350$	−4.02082	−	10.6647i	−0.214922	−	0.570052i
$351$		0			0
$352$	8.67345	−	16.4271i	0.462296	−	0.875567i
$353$	5.36542	−	5.36542i	0.285572	−	0.285572i	−0.549754	−	0.835327i	$-0.685279\pi$
$353$	5.36542	−	5.36542i	0.285572	−	0.285572i	0.835327	+	0.549754i	$0.185279\pi$
$354$		0			0
$355$	31.9832	−	12.9949i	1.69749	−	0.689700i
$356$	14.3247	−	13.2957i	0.759207	−	0.704671i
$357$		0			0
$358$	−12.1370	−	5.29416i	−0.641462	−	0.279805i
$359$			7.76117i			0.409619i	0.978802	+	0.204809i	$0.0656574\pi$
$359$			7.76117i			0.409619i	−0.978802	+	0.204809i	$0.934343\pi$
$360$		0			0
$361$		−	8.34326i		−	0.439119i
$362$	4.67258	−	10.7120i	0.245585	−	0.563012i
$363$		0			0
$364$	0.163823	−	4.39737i	0.00858666	−	0.230485i
$365$	4.34976	+	1.83632i	0.227677	+	0.0961175i
$366$		0			0
$367$	18.0536	−	18.0536i	0.942389	−	0.942389i	−0.0560392	−	0.998429i	$-0.517847\pi$
$367$	18.0536	−	18.0536i	0.942389	−	0.942389i	0.998429	+	0.0560392i	$0.0178472\pi$
$368$	−3.36320	−	3.90554i	−0.175319	−	0.203590i
$369$		0			0
$370$	−7.66698	+	7.28724i	−0.398587	+	0.378845i
$371$	−6.61183	−	6.61183i	−0.343269	−	0.343269i
$372$		0			0
$373$	−4.36197			−0.225854			−0.112927	−	0.993603i	$-0.536023\pi$
$373$	−4.36197			−0.225854			−0.112927	+	0.993603i	$0.536023\pi$
$374$	−12.6089	−	32.1192i	−0.651988	−	1.66084i
$375$		0			0
$376$	29.7419	−	10.4153i	1.53382	−	0.537126i
$377$	3.23979	−	3.23979i	0.166858	−	0.166858i
$378$		0			0
$379$	−5.93072	−	5.93072i	−0.304641	−	0.304641i	0.538186	−	0.842826i	$-0.319110\pi$
$379$	−5.93072	−	5.93072i	−0.304641	−	0.304641i	−0.842826	+	0.538186i	$0.819110\pi$
$380$	7.98998	+	21.9778i	0.409878	+	1.12744i
$381$		0			0
$382$	2.42096	−	0.950385i	0.123867	−	0.0486259i
$383$	19.3340	+	19.3340i	0.987922	+	0.987922i	0.999928	−	0.0120057i	$-0.00382161\pi$
$383$	19.3340	+	19.3340i	0.987922	+	0.987922i	−0.0120057	+	0.999928i	$0.503822\pi$
$384$		0			0
$385$	10.9652	−	4.45520i	0.558836	−	0.227058i
$386$	11.3354	+	4.94449i	0.576957	+	0.251668i
$387$		0			0
$388$	4.62373	+	0.172256i	0.234734	+	0.00874498i
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	−0.848274	−	0.529558i	$-0.822358\pi$
$389$	−6.28607	+	6.28607i	−0.318716	+	0.318716i	0.529558	+	0.848274i	$0.322358\pi$
$390$		0			0
$391$	−9.57367			−0.484161
$392$	−5.39937	+	11.2189i	−0.272709	+	0.566640i
$393$		0			0
$394$	7.31489	−	2.87157i	0.368519	−	0.144668i
$395$	21.3425	−	8.67157i	1.07386	−	0.436314i
$396$		0			0
$397$	6.58413			0.330448			0.165224	−	0.986256i	$-0.447165\pi$
$397$	6.58413			0.330448			0.165224	+	0.986256i	$0.447165\pi$
$398$	−9.16767	+	3.59890i	−0.459534	+	0.180397i
$399$		0			0
$400$	−12.8443	−	15.3305i	−0.642215	−	0.766524i
$401$	−19.7951			−0.988522			−0.494261	−	0.869313i	$-0.664561\pi$
$401$	−19.7951			−0.988522			−0.494261	+	0.869313i	$0.664561\pi$
$402$		0			0
$403$	0.331123			0.0164944
$404$	−18.7664	−	0.699139i	−0.933664	−	0.0347835i
$405$		0			0
$406$	7.12211	−	2.79589i	0.353464	−	0.138758i
$407$	−7.76707	−	7.76707i	−0.385000	−	0.385000i
$408$		0			0
$409$	5.76937			0.285277			0.142638	−	0.989775i	$-0.454441\pi$
$409$	5.76937			0.285277			0.142638	+	0.989775i	$0.454441\pi$
$410$	−6.11892	+	5.81585i	−0.302192	+	0.287225i
$411$		0			0
$412$	−0.170816	+	4.58507i	−0.00841550	+	0.225890i
$413$			13.4826i			0.663437i
$414$		0			0
$415$	6.76563	−	2.74891i	0.332112	−	0.134939i
$416$	−2.27901	−	7.37775i	−0.111738	−	0.361724i
$417$		0			0
$418$	−22.6048	+	8.87385i	−1.10564	+	0.434034i
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	−0.886750	−	0.462249i	$-0.847043\pi$
$419$	−8.68932	+	8.68932i	−0.424501	+	0.424501i	0.462249	+	0.886750i	$0.347043\pi$
$420$		0			0
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	0.999815	−	0.0192594i	$-0.00613083\pi$
$421$	20.1193	+	20.1193i	0.980555	+	0.980555i	−0.0192594	+	0.999815i	$0.506131\pi$
$422$	−4.34513	+	9.96134i	−0.211517	+	0.484911i
$423$		0			0
$424$	−14.7849	−	7.11559i	−0.718017	−	0.345564i
$425$	−37.1466	−	0.502930i	−1.80187	−	0.0243957i
$426$		0			0
$427$	15.2135			0.736231
$428$	5.35349	−	4.96893i	0.258770	−	0.240182i
$429$		0			0
$430$	−20.7407	+	19.7134i	−1.00021	+	0.950667i
$431$		−	33.6247i		−	1.61965i	−0.586675	−	0.809823i	$-0.699563\pi$
$431$		−	33.6247i		−	1.61965i	0.586675	−	0.809823i	$-0.300437\pi$
$432$		0			0
$433$	7.46558	−	7.46558i	0.358773	−	0.358773i	−0.504588	−	0.863361i	$-0.668355\pi$
$433$	7.46558	−	7.46558i	0.358773	−	0.358773i	0.863361	+	0.504588i	$0.168355\pi$
$434$	0.506835	+	0.221081i	0.0243289	+	0.0106122i
$435$		0			0
$436$	−14.7190	−	0.548355i	−0.704914	−	0.0262614i
$437$			6.73775i			0.322310i
$438$		0			0
$439$		−	7.91929i		−	0.377967i	−0.981980	−	0.188984i	$-0.939481\pi$
$439$		−	7.91929i		−	0.377967i	0.981980	−	0.188984i	$-0.0605193\pi$
$440$	15.5762	−	13.7379i	0.742564	−	0.654931i
$441$		0			0
$442$	−13.1468	−	5.73463i	−0.625330	−	0.272768i
$443$			10.6463i			0.505823i	0.967489	+	0.252911i	$0.0813881\pi$
$443$			10.6463i			0.505823i	−0.967489	+	0.252911i	$0.918612\pi$
$444$		0			0
$445$	20.2438	−	8.22517i	0.959649	−	0.389910i
$446$	−6.89106	+	15.7980i	−0.326301	+	0.748056i
$447$		0			0
$448$	1.43752	−	12.8144i	0.0679164	−	0.605424i
$449$			6.08115i			0.286987i	0.989651	+	0.143494i	$0.0458336\pi$
$449$			6.08115i			0.286987i	−0.989651	+	0.143494i	$0.954166\pi$
$450$		0			0
$451$	−6.19880	−	6.19880i	−0.291890	−	0.291890i
$452$	−0.450582	+	12.0946i	−0.0211936	+	0.568882i
$453$		0			0
$454$	7.92450	−	3.11088i	0.371915	−	0.146001i
$455$	1.91346	−	4.53247i	0.0897042	−	0.212485i
$456$		0			0
$457$	0.313815	−	0.313815i	0.0146796	−	0.0146796i	−0.699729	−	0.714409i	$-0.746696\pi$
$457$	0.313815	−	0.313815i	0.0146796	−	0.0146796i	0.714409	+	0.699729i	$0.246696\pi$
$458$	−1.04218	−	0.454596i	−0.0486977	−	0.0212419i
$459$		0			0
$460$	−1.96884	−	5.41564i	−0.0917977	−	0.252505i
$461$	−9.90949	+	9.90949i	−0.461531	+	0.461531i	−0.899157	−	0.437626i	$-0.855819\pi$
$461$	−9.90949	+	9.90949i	−0.461531	+	0.461531i	0.437626	+	0.899157i	$0.355819\pi$
$462$		0			0
$463$	17.3430	+	17.3430i	0.805999	+	0.805999i	0.984026	−	0.178027i	$-0.0569714\pi$
$463$	17.3430	+	17.3430i	0.805999	+	0.805999i	−0.178027	+	0.984026i	$0.556971\pi$
$464$	10.1738	−	8.76103i	0.472307	−	0.406720i
$465$		0			0
$466$	10.1537	−	23.2777i	0.470361	−	1.07832i
$467$		−	1.52267i		−	0.0704606i	−0.999379	−	0.0352303i	$-0.988784\pi$
$467$		−	1.52267i		−	0.0704606i	0.999379	−	0.0352303i	$-0.0112165\pi$
$468$		0			0
$469$	−5.18213	+	5.18213i	−0.239289	+	0.239289i
$470$	35.2210	+	0.894381i	1.62463	+	0.0412547i
$471$		0			0
$472$	7.81950	+	22.3294i	0.359921	+	1.02779i
$473$	−21.0115	−	21.0115i	−0.966110	−	0.966110i
$474$		0			0
$475$	−0.353952	+	26.1430i	−0.0162404	+	1.19952i
$476$	−16.2944	−	17.5555i	−0.746852	−	0.804653i
$477$		0			0
$478$	−0.921443	−	2.34724i	−0.0421458	−	0.107360i
$479$	−0.507657			−0.0231955			−0.0115977	−	0.999933i	$-0.503692\pi$
$479$	−0.507657			−0.0231955			−0.0115977	+	0.999933i	$0.503692\pi$
$480$		0			0
$481$	−4.56592			−0.208188
$482$	5.39720	+	13.7486i	0.245836	+	0.626229i
$483$		0			0
$484$	−0.294297	−	0.317074i	−0.0133772	−	0.0144125i
$485$	4.76578	+	2.01195i	0.216403	+	0.0913581i
$486$		0			0
$487$	−25.9809	−	25.9809i	−1.17730	−	1.17730i	−0.980428	−	0.196876i	$-0.936920\pi$
$487$	−25.9809	−	25.9809i	−1.17730	−	1.17730i	−0.196876	−	0.980428i	$-0.563080\pi$
$488$	25.1959	−	8.82332i	1.14057	−	0.399413i
$489$		0			0
$490$	−10.0897	+	9.59000i	−0.455808	+	0.433232i
$491$	3.28208	−	3.28208i	0.148118	−	0.148118i	−0.629159	−	0.777277i	$-0.716600\pi$
$491$	3.28208	−	3.28208i	0.148118	−	0.148118i	0.777277	+	0.629159i	$0.216600\pi$
$492$		0			0
$493$		−	24.9391i		−	1.12320i
$494$	−4.03591	+	9.25246i	−0.181584	+	0.416288i
$495$		0			0
$496$	0.967619	+	0.0721971i	0.0434474	+	0.00324175i
$497$	17.5964	+	17.5964i	0.789308	+	0.789308i
$498$		0			0
$499$	−6.73907	+	6.73907i	−0.301682	+	0.301682i	−0.841672	−	0.539990i	$-0.818428\pi$
$499$	−6.73907	+	6.73907i	−0.301682	+	0.301682i	0.539990	+	0.841672i	$0.318428\pi$
$500$	−7.35476	−	21.1165i	−0.328915	−	0.944360i
$501$		0			0
$502$	23.1894	+	10.1152i	1.03499	+	0.451463i
$503$	6.12090	−	6.12090i	0.272918	−	0.272918i	−0.557356	−	0.830274i	$-0.688184\pi$
$503$	6.12090	−	6.12090i	0.272918	−	0.272918i	0.830274	+	0.557356i	$0.188184\pi$
$504$		0			0
$505$	−19.3430	−	8.16596i	−0.860752	−	0.363380i
$506$	5.57013	−	2.18664i	0.247623	−	0.0972079i
$507$		0			0
$508$	0.767904	−	20.6122i	0.0340702	−	0.914519i
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	0.329323	−	0.944217i	$-0.393180\pi$
$509$	−13.8727	−	13.8727i	−0.614894	−	0.614894i	−0.944217	+	0.329323i	$0.893180\pi$
$510$		0			0
$511$			3.40344i			0.150559i
$512$	−5.05119	−	22.0564i	−0.223233	−	0.974765i
$513$		0			0
$514$	−3.30299	+	7.57221i	−0.145689	+	0.333996i
$515$	−1.99514	+	4.72594i	−0.0879162	+	0.208250i
$516$		0			0
$517$			36.5869i			1.60909i
$518$	−6.98884	−	3.04853i	−0.307072	−	0.133945i
$519$		0			0
$520$	0.540302	−	8.61623i	0.0236938	−	0.377847i
$521$			5.87686i			0.257470i	0.991679	+	0.128735i	$0.0410917\pi$
$521$			5.87686i			0.257470i	−0.991679	+	0.128735i	$0.958908\pi$
$522$		0			0
$523$			26.0176i			1.13767i	0.822452	+	0.568834i	$0.192605\pi$
$523$			26.0176i			1.13767i	−0.822452	+	0.568834i	$0.807395\pi$
$524$	−33.8591	−	1.26141i	−1.47914	−	0.0551051i
$525$		0			0
$526$	−31.4030	−	13.6980i	−1.36924	−	0.597260i
$527$	1.27445	−	1.27445i	0.0555160	−	0.0555160i
$528$		0			0
$529$			21.3397i			0.927814i
$530$	−12.6382	−	13.2968i	−0.548970	−	0.577577i
$531$		0			0
$532$	−12.3552	+	11.4677i	−0.535665	+	0.497186i
$533$	−3.64400			−0.157839
$534$		0			0
$535$	7.56561	−	3.07394i	0.327090	−	0.132898i
$536$	−5.57696	+	11.5879i	−0.240888	+	0.500521i
$537$		0			0
$538$	−15.8388	+	36.3109i	−0.682858	+	1.56547i
$539$	−10.2215	−	10.2215i	−0.440270	−	0.440270i
$540$		0			0
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	−0.834210	−	0.551447i	$-0.814076\pi$
$541$	−6.57691	+	6.57691i	−0.282764	+	0.282764i	0.551447	+	0.834210i	$0.314076\pi$
$542$	36.7992	−	14.4461i	1.58066	−	0.620513i
$543$		0			0
$544$	−37.1677	−	19.6244i	−1.59355	−	0.841390i
$545$	−15.1712	−	6.40479i	−0.649865	−	0.274351i
$546$		0			0
$547$		−	10.6170i		−	0.453951i	−0.973900	−	0.226976i	$-0.927116\pi$
$547$		−	10.6170i		−	0.453951i	0.973900	−	0.226976i	$-0.0728838\pi$
$548$	−0.518876	+	13.9277i	−0.0221653	+	0.594964i
$549$		0			0
$550$	21.7274	−	8.19171i	0.926460	−	0.349296i
$551$	−17.5516			−0.747724
$552$		0			0
$553$	11.7422	+	11.7422i	0.499328	+	0.499328i
$554$	34.2605	−	13.4495i	1.45559	−	0.571414i
$555$		0			0
$556$	−29.1168	−	1.08474i	−1.23483	−	0.0460033i
$557$	−20.9610			−0.888146			−0.444073	−	0.895991i	$-0.646467\pi$
$557$	−20.9610			−0.888146			−0.444073	+	0.895991i	$0.646467\pi$
$558$		0			0
$559$	−12.3517			−0.522422
$560$	6.57981	−	12.8277i	0.278048	−	0.542070i
$561$		0			0
$562$	31.7257	−	12.4544i	1.33827	−	0.525356i
$563$	−16.5598			−0.697911			−0.348955	−	0.937139i	$-0.613464\pi$
$563$	−16.5598			−0.697911			−0.348955	+	0.937139i	$0.613464\pi$
$564$		0			0
$565$	−5.26280	+	12.4662i	−0.221408	+	0.524456i
$566$	6.23594	−	2.44801i	0.262116	−	0.102898i
$567$		0			0
$568$	39.3479	+	18.9371i	1.65100	+	0.794584i
$569$	39.6751			1.66327			0.831634	−	0.555325i	$-0.187406\pi$
$569$	39.6751			1.66327			0.831634	+	0.555325i	$0.187406\pi$
$570$		0			0
$571$	24.0292	−	24.0292i	1.00559	−	1.00559i	0.00560819	−	0.999984i	$-0.498215\pi$
$571$	24.0292	−	24.0292i	1.00559	−	1.00559i	0.999984	−	0.00560819i	$-0.00178515\pi$
$572$	8.95885	+	0.333760i	0.374588	+	0.0139552i
$573$		0			0
$574$	−5.57771	−	2.43299i	−0.232809	−	0.101551i
$575$	0.0872185	−	6.44199i	0.00363726	−	0.268649i
$576$		0			0
$577$	−28.7705	−	28.7705i	−1.19773	−	1.19773i	−0.974844	−	0.222888i	$-0.928451\pi$
$577$	−28.7705	−	28.7705i	−1.19773	−	1.19773i	−0.222888	−	0.974844i	$-0.571549\pi$
$578$	−50.2933	+	19.7434i	−2.09193	+	0.821217i
$579$		0			0
$580$	14.1076	−	5.12877i	0.585785	−	0.212960i
$581$	3.72230	+	3.72230i	0.154427	+	0.154427i
$582$		0			0
$583$	13.4704	−	13.4704i	0.557888	−	0.557888i
$584$	1.97389	+	5.63664i	0.0816800	+	0.233246i
$585$		0			0
$586$	1.60718	+	4.09406i	0.0663922	+	0.169124i
$587$	−33.4854			−1.38209			−0.691046	−	0.722811i	$-0.742850\pi$
$587$	−33.4854			−1.38209			−0.691046	+	0.722811i	$0.742850\pi$
$588$		0			0
$589$	−0.896933	−	0.896933i	−0.0369575	−	0.0369575i
$590$	−0.671477	+	26.4430i	−0.0276443	+	1.08864i
$591$		0			0
$592$	−13.3427	−	0.995540i	−0.548381	−	0.0409164i
$593$	−11.5298	+	11.5298i	−0.473472	+	0.473472i	−0.903036	−	0.429564i	$-0.858667\pi$
$593$	−11.5298	+	11.5298i	−0.473472	+	0.473472i	0.429564	+	0.903036i	$0.358667\pi$
$594$		0			0
$595$	−10.0803	−	24.8096i	−0.413250	−	1.01709i
$596$	−1.60097	+	42.9735i	−0.0655783	+	1.76026i
$597$		0			0
$598$	0.994503	−	2.27993i	0.0406683	−	0.0932333i
$599$		−	20.0148i		−	0.817781i	−0.912583	−	0.408891i	$-0.865916\pi$
$599$		−	20.0148i		−	0.817781i	0.912583	−	0.408891i	$-0.134084\pi$
$600$		0			0
$601$		−	27.5924i		−	1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$601$		−	27.5924i		−	1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$602$	−18.9062	−	8.24688i	−0.770560	−	0.336118i
$603$		0			0
$604$	15.6931	−	14.5658i	0.638542	−	0.592673i
$605$	−0.182062	−	0.448093i	−0.00740188	−	0.0182176i
$606$		0			0
$607$	−30.4850	+	30.4850i	−1.23735	+	1.23735i	−0.276265	+	0.961081i	$0.589097\pi$
$607$	−30.4850	+	30.4850i	−1.23735	+	1.23735i	−0.961081	+	0.276265i	$0.910903\pi$
$608$	−13.8113	+	26.1579i	−0.560120	+	1.06084i
$609$		0			0
$610$	29.8376	+	0.757677i	1.20809	+	0.0306774i
$611$	10.7539	+	10.7539i	0.435057	+	0.435057i
$612$		0			0
$613$	−20.2657			−0.818523			−0.409261	−	0.912417i	$-0.634214\pi$
$613$	−20.2657			−0.818523			−0.409261	+	0.912417i	$0.634214\pi$
$614$	−19.1762	+	7.52788i	−0.773887	+	0.303801i
$615$		0			0
$616$	13.4901	+	6.49242i	0.543530	+	0.261587i
$617$	−1.61302	+	1.61302i	−0.0649378	+	0.0649378i	−0.738830	−	0.673892i	$-0.764621\pi$
$617$	−1.61302	+	1.61302i	−0.0649378	+	0.0649378i	0.673892	+	0.738830i	$0.264621\pi$
$618$		0			0
$619$	−2.46756	−	2.46756i	−0.0991797	−	0.0991797i	0.655776	−	0.754956i	$-0.272342\pi$
$619$	−2.46756	−	2.46756i	−0.0991797	−	0.0991797i	−0.754956	+	0.655776i	$0.772342\pi$
$620$	0.983026	+	0.458839i	0.0394793	+	0.0184274i
$621$		0			0
$622$	7.47114	+	19.0316i	0.299565	+	0.763098i
$623$	11.1377	+	11.1377i	0.446222	+	0.446222i
$624$		0			0
$625$	0.676829	−	24.9908i	0.0270732	−	0.999633i
$626$	8.09815	−	18.5653i	0.323667	−	0.742017i
$627$		0			0
$628$	−3.43879	+	3.19177i	−0.137222	+	0.127365i
$629$	−17.5737	+	17.5737i	−0.700708	+	0.700708i
$630$		0			0
$631$	−29.9602			−1.19270			−0.596348	−	0.802726i	$-0.703382\pi$
$631$	−29.9602			−1.19270			−0.596348	+	0.802726i	$0.703382\pi$
$632$	26.2570	+	12.6368i	1.04445	+	0.502666i
$633$		0			0
$634$	7.17026	+	18.2652i	0.284767	+	0.725402i
$635$	8.96913	−	21.2455i	0.355929	−	0.843101i
$636$		0			0
$637$	−6.00875			−0.238075
$638$	5.69612	+	14.5100i	0.225512	+	0.574457i
$639$		0			0
$640$	3.45755	−	25.0608i	0.136672	−	0.990616i
$641$	37.3386			1.47478			0.737392	−	0.675465i	$-0.236057\pi$
$641$	37.3386			1.47478			0.737392	+	0.675465i	$0.236057\pi$
$642$		0			0
$643$	24.5635			0.968691			0.484345	−	0.874877i	$-0.339058\pi$
$643$	24.5635			0.968691			0.484345	+	0.874877i	$0.339058\pi$
$644$	3.04448	−	2.82579i	0.119969	−	0.111352i
$645$		0			0
$646$	20.0778	+	51.1453i	0.789952	+	2.01229i
$647$	23.1347	+	23.1347i	0.909519	+	0.909519i	0.996233	−	0.0867142i	$-0.0276367\pi$
$647$	23.1347	+	23.1347i	0.909519	+	0.909519i	−0.0867142	+	0.996233i	$0.527637\pi$
$648$		0			0
$649$	−27.4685			−1.07823
$650$	3.97852	−	8.79406i	0.156050	−	0.344932i
$651$		0			0
$652$	4.01101	−	3.72289i	0.157083	−	0.145800i
$653$		−	50.8060i		−	1.98819i	−0.108496	−	0.994097i	$-0.534603\pi$
$653$		−	50.8060i		−	1.98819i	0.108496	−	0.994097i	$-0.465397\pi$
$654$		0			0
$655$	−34.8993	−	14.7333i	−1.36363	−	0.575679i
$656$	−10.6486	−	0.794528i	−0.415759	−	0.0310211i
$657$		0			0
$658$	9.28047	+	23.6406i	0.361790	+	0.921607i
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	−0.485537	−	0.874216i	$-0.661376\pi$
$659$	9.97780	−	9.97780i	0.388680	−	0.388680i	0.874216	+	0.485537i	$0.161376\pi$
$660$		0			0
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	0.601012	−	0.799240i	$-0.294764\pi$
$661$	−5.09643	−	5.09643i	−0.198228	−	0.198228i	−0.799240	+	0.601012i	$0.794764\pi$
$662$	3.10648	+	1.35505i	0.120737	+	0.0526653i
$663$		0			0
$664$	8.32353	+	4.00590i	0.323015	+	0.155459i
$665$	−17.4605	+	7.09428i	−0.677088	+	0.275104i
$666$		0			0
$667$	4.32496			0.167463
$668$	28.6399	+	1.06697i	1.10811	+	0.0412825i
$669$		0			0
$670$	−10.4216	+	9.90543i	−0.402622	+	0.382680i
$671$			30.9947i			1.19654i
$672$		0			0
$673$	−31.6322	+	31.6322i	−1.21933	+	1.21933i	−0.251464	+	0.967867i	$0.580912\pi$
$673$	−31.6322	+	31.6322i	−1.21933	+	1.21933i	−0.967867	+	0.251464i	$0.919088\pi$
$674$	7.62323	−	17.4765i	0.293636	−	0.673169i
$675$		0			0
$676$	−16.3251	+	15.1524i	−0.627889	+	0.582786i
$677$		−	25.6600i		−	0.986196i	−0.869974	−	0.493098i	$-0.835864\pi$
$677$		−	25.6600i		−	0.986196i	0.869974	−	0.493098i	$-0.164136\pi$
$678$		0			0
$679$			3.72896i			0.143104i
$680$	−31.0833	−	35.2424i	−1.19199	−	1.35148i
$681$		0			0
$682$	−0.450413	+	1.03259i	−0.0172472	+	0.0395397i
$683$			12.3536i			0.472698i	0.971668	+	0.236349i	$0.0759509\pi$
$683$			12.3536i			0.472698i	−0.971668	+	0.236349i	$0.924049\pi$
$684$		0			0
$685$	−6.06048	+	14.3557i	−0.231559	+	0.548501i
$686$	−23.8230	−	10.3915i	−0.909564	−	0.396751i
$687$		0			0
$688$	−36.0946	−	2.69314i	−1.37610	−	0.102675i
$689$		−	7.91866i		−	0.301677i
$690$		0			0
$691$	22.5426	+	22.5426i	0.857561	+	0.857561i	0.991050	−	0.133489i	$-0.0426180\pi$
$691$	22.5426	+	22.5426i	0.857561	+	0.857561i	−0.133489	+	0.991050i	$0.542618\pi$
$692$	11.9676	+	12.8938i	0.454938	+	0.490147i
$693$		0			0
$694$	3.44831	+	8.78406i	0.130896	+	0.333438i
$695$	−30.0114	−	12.6698i	−1.13840	−	0.480593i
$696$		0			0
$697$	−14.0253	+	14.0253i	−0.531247	+	0.531247i
$698$	−1.62021	+	3.71438i	−0.0613258	+	0.140591i
$699$		0			0
$700$	11.9613	−	10.8043i	0.452094	−	0.408365i
$701$	−26.9530	+	26.9530i	−1.01800	+	1.01800i	−0.0181663	+	0.999835i	$0.505783\pi$
$701$	−26.9530	+	26.9530i	−1.01800	+	1.01800i	−0.999835	+	0.0181663i	$0.994217\pi$
$702$		0			0
$703$	12.3680	+	12.3680i	0.466467	+	0.466467i
$704$	26.1071	+	2.92869i	0.983947	+	0.110379i
$705$		0			0
$706$	9.83583	+	4.29038i	0.370176	+	0.161471i
$707$		−	15.1348i		−	0.569203i
$708$		0			0
$709$	7.78615	−	7.78615i	0.292415	−	0.292415i	−0.545619	−	0.838034i	$-0.683705\pi$
$709$	7.78615	−	7.78615i	0.292415	−	0.292415i	0.838034	+	0.545619i	$0.183705\pi$
$710$	33.6349	+	35.3876i	1.26229	+	1.32807i
$711$		0			0
$712$	24.9053	+	11.9863i	0.933365	+	0.449205i
$713$	0.221016	+	0.221016i	0.00827713	+	0.00827713i
$714$		0			0
$715$	9.23410	+	3.89833i	0.345336	+	0.145789i
$716$	0.697158	−	18.7132i	0.0260540	−	0.699346i
$717$		0			0
$718$	−10.2169	+	4.01079i	−0.381291	+	0.149681i
$719$	−20.6777			−0.771150			−0.385575	−	0.922677i	$-0.625997\pi$
$719$	−20.6777			−0.771150			−0.385575	+	0.922677i	$0.625997\pi$
$720$		0			0
$721$	−3.69779			−0.137713
$722$	10.9832	−	4.31161i	0.408751	−	0.160461i
$723$		0			0
$724$	16.5161	+	0.615306i	0.613817	+	0.0228677i
$725$	16.7812	+	0.227201i	0.623237	+	0.00843805i
$726$		0			0
$727$	20.4994	+	20.4994i	0.760280	+	0.760280i	0.976373	−	0.216093i	$-0.0693315\pi$
$727$	20.4994	+	20.4994i	0.760280	+	0.760280i	−0.216093	+	0.976373i	$0.569331\pi$
$728$	5.87341	−	2.05680i	0.217683	−	0.0762301i
$729$		0			0
$730$	−0.169502	+	6.67505i	−0.00627355	+	0.247055i
$731$	−47.5403	+	47.5403i	−1.75834	+	1.75834i
$732$		0			0
$733$		−	10.7306i		−	0.396344i	−0.980167	−	0.198172i	$-0.936500\pi$
$733$		−	10.7306i		−	0.396344i	0.980167	−	0.198172i	$-0.0635005\pi$
$734$	33.0956	+	14.4363i	1.22158	+	0.532853i
$735$		0			0
$736$	3.40328	−	6.44565i	0.125447	−	0.237590i
$737$	−10.5577	−	10.5577i	−0.388897	−	0.388897i
$738$		0			0
$739$	2.93837	−	2.93837i	0.108090	−	0.108090i	−0.650994	−	0.759083i	$-0.725648\pi$
$739$	2.93837	−	2.93837i	0.108090	−	0.108090i	0.759083	+	0.650994i	$0.225648\pi$
$740$	−13.5551	−	6.32702i	−0.498296	−	0.232586i
$741$		0			0
$742$	5.28705	−	12.1207i	0.194094	−	0.444966i
$743$	0.223404	−	0.223404i	0.00819590	−	0.00819590i	−0.702997	−	0.711193i	$-0.748155\pi$
$743$	0.223404	−	0.223404i	0.00819590	−	0.00819590i	0.711193	+	0.702997i	$0.248155\pi$
$744$		0			0
$745$	−18.6994	+	44.2938i	−0.685091	+	1.62280i
$746$	−2.25416	−	5.74215i	−0.0825308	−	0.210235i
$747$		0			0
$748$	35.7661	−	33.1969i	1.30774	−	1.21380i
$749$	4.16243	+	4.16243i	0.152092	+	0.152092i
$750$		0			0
$751$			39.9939i			1.45940i	0.683769	+	0.729699i	$0.260340\pi$
$751$			39.9939i			1.45940i	−0.683769	+	0.729699i	$0.739660\pi$
$752$	29.0807	+	33.7702i	1.06046	+	1.23147i
$753$		0			0
$754$	5.93915	+	2.59065i	0.216291	+	0.0943459i
$755$	22.1776	−	9.01088i	0.807126	−	0.327939i
$756$		0			0
$757$			32.9120i			1.19621i	0.801419	+	0.598103i	$0.204079\pi$
$757$			32.9120i			1.19621i	−0.801419	+	0.598103i	$0.795921\pi$
$758$	4.74241	−	10.8721i	0.172252	−	0.394894i
$759$		0			0
$760$	−24.8029	+	21.8758i	−0.899694	+	0.793517i
$761$			33.9591i			1.23102i	0.788130	+	0.615509i	$0.211049\pi$
$761$			33.9591i			1.23102i	−0.788130	+	0.615509i	$0.788951\pi$
$762$		0			0
$763$		−	11.8707i		−	0.429747i
$764$	2.50220	+	2.69585i	0.0905263	+	0.0975324i
$765$		0			0
$766$	−15.4602	+	35.4429i	−0.558598	+	1.28060i
$767$	−8.07375	+	8.07375i	−0.291526	+	0.291526i
$768$		0			0
$769$		−	40.2535i		−	1.45158i	−0.687917	−	0.725789i	$-0.741475\pi$
$769$		−	40.2535i		−	1.45158i	0.687917	−	0.725789i	$-0.258525\pi$
$770$	11.5314	+	12.1323i	0.415563	+	0.437218i
$771$		0			0
$772$	−0.651112	+	17.4773i	−0.0234340	+	0.629020i
$773$	−9.47175			−0.340675			−0.170338	−	0.985386i	$-0.554486\pi$
$773$	−9.47175			−0.340675			−0.170338	+	0.985386i	$0.554486\pi$
$774$		0			0
$775$	0.845950	+	0.869172i	0.0303874	+	0.0312216i
$776$	2.16268	+	6.17575i	0.0776355	+	0.221696i
$777$		0			0
$778$	−11.5236	−	5.02656i	−0.413139	−	0.180211i
$779$	9.87073	+	9.87073i	0.353656	+	0.353656i
$780$		0			0
$781$	−35.8496	+	35.8496i	−1.28280	+	1.28280i
$782$	−4.94745	−	12.6029i	−0.176921	−	0.450679i
$783$		0			0
$784$	−17.5590	−	1.31013i	−0.627106	−	0.0467904i
$785$	−4.85973	+	1.97453i	−0.173451	+	0.0704741i
$786$		0			0
$787$		−	48.1367i		−	1.71589i	−0.513742	−	0.857945i	$-0.671741\pi$
$787$		−	48.1367i		−	1.71589i	0.513742	−	0.857945i	$-0.328259\pi$
$788$	7.56034	+	8.14546i	0.269326	+	0.290170i
$789$		0			0
$790$	22.4447	+	23.6143i	0.798546	+	0.840158i
$791$	−9.75409			−0.346815
$792$		0			0
$793$	9.11021	+	9.11021i	0.323513	+	0.323513i
$794$	3.40253	+	8.66743i	0.120751	+	0.307596i
$795$		0			0
$796$	−9.47528	−	10.2086i	−0.335842	−	0.361834i
$797$	33.8962			1.20066			0.600332	−	0.799751i	$-0.295035\pi$
$797$	33.8962			1.20066			0.600332	+	0.799751i	$0.295035\pi$
$798$		0			0
$799$	82.7810			2.92858
$800$	13.5436	−	24.8308i	0.478839	−	0.877903i
$801$		0			0
$802$	−10.2297	−	26.0586i	−0.361222	−	0.920160i
$803$	−6.93391			−0.244692
$804$		0			0
$805$	4.30250	−	1.74813i	0.151643	−	0.0616133i
$806$	0.171117	+	0.435894i	0.00602733	+	0.0153537i
$807$		0			0
$808$	−8.77770	−	25.0656i	−0.308798	−	0.881806i
$809$	−27.5625			−0.969047			−0.484523	−	0.874778i	$-0.661007\pi$
$809$	−27.5625			−0.969047			−0.484523	+	0.874778i	$0.661007\pi$
$810$		0			0
$811$	−24.1817	+	24.1817i	−0.849133	+	0.849133i	−0.990025	−	0.140892i	$-0.955003\pi$
$811$	−24.1817	+	24.1817i	−0.849133	+	0.849133i	0.140892	+	0.990025i	$0.455003\pi$
$812$	7.36108	+	7.93078i	0.258323	+	0.278316i
$813$		0			0
$814$	6.21083	−	14.2385i	0.217689	−	0.499060i
$815$	5.66841	−	2.30310i	0.198556	−	0.0806742i
$816$		0			0
$817$	33.4579	+	33.4579i	1.17054	+	1.17054i
$818$	2.98148	+	7.59486i	0.104245	+	0.265548i
$819$		0			0
$820$	−10.8182	−	5.04952i	−0.377787	−	0.176337i
$821$	−0.0575735	−	0.0575735i	−0.00200933	−	0.00200933i	0.706101	−	0.708111i	$-0.250452\pi$
$821$	−0.0575735	−	0.0575735i	−0.00200933	−	0.00200933i	−0.708111	+	0.706101i	$0.750452\pi$
$822$		0			0
$823$	28.5594	−	28.5594i	0.995518	−	0.995518i	−0.00447159	−	0.999990i	$-0.501423\pi$
$823$	28.5594	−	28.5594i	0.995518	−	0.995518i	0.999990	+	0.00447159i	$0.00142335\pi$
$824$	−6.12412	+	2.14460i	−0.213344	+	0.0747106i
$825$		0			0
$826$	−17.7487	+	6.96752i	−0.617557	+	0.242431i
$827$	23.0863			0.802788			0.401394	−	0.915905i	$-0.368526\pi$
$827$	23.0863			0.802788			0.401394	+	0.915905i	$0.368526\pi$
$828$		0			0
$829$	−33.3543	−	33.3543i	−1.15844	−	1.15844i	−0.984811	−	0.173631i	$-0.944450\pi$
$829$	−33.3543	−	33.3543i	−1.15844	−	1.15844i	−0.173631	−	0.984811i	$-0.555550\pi$
$830$	7.11502	+	7.48578i	0.246966	+	0.259835i
$831$		0			0
$832$	8.53442	−	6.81277i	0.295878	−	0.236190i
$833$	−23.1269	+	23.1269i	−0.801301	+	0.801301i
$834$		0			0
$835$	29.5198	+	12.4623i	1.02158	+	0.431275i
$836$	−23.3633	−	25.1715i	−0.808037	−	0.870573i
$837$		0			0
$838$	−15.9292	−	6.94829i	−0.550264	−	0.240025i
$839$		−	49.4524i		−	1.70729i	−0.520859	−	0.853643i	$-0.674388\pi$
$839$		−	49.4524i		−	1.70729i	0.520859	−	0.853643i	$-0.325612\pi$
$840$		0			0
$841$		−	17.7336i		−	0.611504i
$842$	−16.0881	+	36.8825i	−0.554433	+	1.27106i
$843$		0			0
$844$	−15.3587	−	0.572185i	−0.528668	−	0.0196954i
$845$	−23.0708	+	9.37380i	−0.793661	+	0.322469i
$846$		0			0
$847$	0.246530	−	0.246530i	0.00847089	−	0.00847089i
$848$	1.72656	−	23.1402i	0.0592904	−	0.794637i
$849$		0			0
$850$	−18.5344	−	49.1601i	−0.635726	−	1.68618i
$851$	−3.04764	−	3.04764i	−0.104472	−	0.104472i
$852$		0			0
$853$	−31.3639			−1.07388			−0.536939	−	0.843621i	$-0.680419\pi$
$853$	−31.3639			−1.07388			−0.536939	+	0.843621i	$0.680419\pi$
$854$	7.86197	+	20.0272i	0.269031	+	0.685316i
$855$		0			0
$856$	9.30771	+	4.47957i	0.318131	+	0.153108i
$857$	−16.1594	+	16.1594i	−0.551996	+	0.551996i	−0.927016	−	0.375021i	$-0.877636\pi$
$857$	−16.1594	+	16.1594i	−0.551996	+	0.551996i	0.375021	+	0.927016i	$0.377636\pi$
$858$		0			0
$859$	−30.7369	−	30.7369i	−1.04873	−	1.04873i	−0.998750	−	0.0499792i	$-0.984085\pi$
$859$	−30.7369	−	30.7369i	−1.04873	−	1.04873i	−0.0499792	−	0.998750i	$-0.515915\pi$
$860$	−36.6694	−	17.1159i	−1.25041	−	0.583647i
$861$		0			0
$862$	44.2640	−	17.3765i	1.50764	−	0.591845i
$863$	18.9353	+	18.9353i	0.644565	+	0.644565i	0.951674	−	0.307109i	$-0.0993618\pi$
$863$	18.9353	+	18.9353i	0.644565	+	0.644565i	−0.307109	+	0.951674i	$0.599362\pi$
$864$		0			0
$865$	7.40353	+	18.2216i	0.251728	+	0.619553i
$866$	13.6858	+	5.96974i	0.465063	+	0.202860i
$867$		0			0
$868$	−0.0291129	+	0.781453i	−0.000988156	+	0.0265242i
$869$	−23.9226	+	23.9226i	−0.811517	+	0.811517i
$870$		0			0
$871$	−6.20638			−0.210295
$872$	−6.88460	−	19.6597i	−0.233142	−	0.665761i
$873$		0			0
$874$	−8.86966	+	3.48191i	−0.300021	+	0.117778i
$875$	16.7859	−	6.55684i	0.567465	−	0.221662i
$876$		0			0
$877$	49.7461			1.67981			0.839903	−	0.542737i	$-0.182612\pi$
$877$	49.7461			1.67981			0.839903	+	0.542737i	$0.182612\pi$
$878$	10.4250	−	4.09251i	0.351828	−	0.138115i
$879$		0			0
$880$	26.1342	+	13.4052i	0.880984	+	0.451889i
$881$	−27.7694			−0.935574			−0.467787	−	0.883841i	$-0.654949\pi$
$881$	−27.7694			−0.935574			−0.467787	+	0.883841i	$0.654949\pi$
$882$		0			0
$883$	−42.4602			−1.42890			−0.714450	−	0.699686i	$-0.753323\pi$
$883$	−42.4602			−1.42890			−0.714450	+	0.699686i	$0.753323\pi$
$884$	0.755161	−	20.2702i	0.0253988	−	0.681759i
$885$		0			0
$886$	−14.0150	+	5.50178i	−0.470842	+	0.184836i
$887$	16.1076	+	16.1076i	0.540842	+	0.540842i	0.923776	−	0.382934i	$-0.125086\pi$
$887$	16.1076	+	16.1076i	0.540842	+	0.540842i	−0.382934	+	0.923776i	$0.625086\pi$
$888$		0			0
$889$	16.6234			0.557531
$890$	21.2893	+	22.3986i	0.713617	+	0.750804i
$891$		0			0
$892$	−24.3578	−	0.907445i	−0.815560	−	0.0303835i
$893$		−	58.2596i		−	1.94958i
$894$		0			0
$895$	8.14281	−	19.2882i	0.272184	−	0.644732i
$896$	17.6119	−	4.72983i	0.588373	−	0.158012i
$897$		0			0
$898$	−8.00530	+	3.14260i	−0.267140	+	0.104870i
$899$	−0.575741	+	0.575741i	−0.0192020	+	0.0192020i
$900$		0			0
$901$	−30.4780	−	30.4780i	−1.01537	−	1.01537i
$902$	4.95678	−	11.3636i	0.165043	−	0.378366i
$903$		0			0
$904$	−16.1543	+	5.65706i	−0.537285	+	0.188151i
$905$	17.0236	+	7.18678i	0.565883	+	0.238897i
$906$		0			0
$907$	−9.20991			−0.305810			−0.152905	−	0.988241i	$-0.548863\pi$
$907$	−9.20991			−0.305810			−0.152905	+	0.988241i	$0.548863\pi$
$908$	8.19040	+	8.82427i	0.271808	+	0.292844i
$909$		0			0
$910$	6.95543	+	0.176622i	0.230570	+	0.00585495i
$911$		−	45.8065i		−	1.51764i	−0.651302	−	0.758819i	$-0.725777\pi$
$911$		−	45.8065i		−	1.51764i	0.651302	−	0.758819i	$-0.274223\pi$
$912$		0			0
$913$	−7.58351	+	7.58351i	−0.250978	+	0.250978i
$914$	0.575282	+	0.250938i	0.0190286	+	0.00830028i
$915$		0			0
$916$	0.0598632	−	1.60686i	0.00197794	−	0.0530921i
$917$		−	27.3068i		−	0.901749i
$918$		0			0
$919$			5.52468i			0.182242i	0.995840	+	0.0911211i	$0.0290450\pi$
$919$			5.52468i			0.182242i	−0.995840	+	0.0911211i	$0.970955\pi$
$920$	6.11176	−	5.39048i	0.201499	−	0.177719i
$921$		0			0
$922$	−18.1660	−	7.92398i	−0.598264	−	0.260962i
$923$			21.0744i			0.693672i
$924$		0			0
$925$	−11.6650	−	11.9852i	−0.383542	−	0.394070i
$926$	−13.8681	+	31.7930i	−0.455734	+	1.04478i
$927$		0			0
$928$	16.7907	+	8.86544i	0.551182	+	0.291022i
$929$		−	43.4288i		−	1.42485i	−0.701746	−	0.712427i	$-0.747596\pi$
$929$		−	43.4288i		−	1.42485i	0.701746	−	0.712427i	$-0.252404\pi$
$930$		0			0
$931$	16.2763	+	16.2763i	0.533433	+	0.533433i
$932$	35.8903	+	1.33708i	1.17562	+	0.0437977i
$933$		0			0
$934$	2.00446	−	0.786879i	0.0655878	−	0.0257475i
$935$	50.5451	−	20.5367i	1.65300	−	0.671623i
$936$		0			0
$937$	20.7275	−	20.7275i	0.677138	−	0.677138i	−0.282213	−	0.959352i	$-0.591069\pi$
$937$	20.7275	−	20.7275i	0.677138	−	0.677138i	0.959352	+	0.282213i	$0.0910686\pi$
$938$	−9.49983	−	4.14381i	−0.310180	−	0.135300i
$939$		0			0
$940$	17.0241	+	46.8276i	0.555264	+	1.52735i
$941$	−12.3393	+	12.3393i	−0.402251	+	0.402251i	−0.879026	−	0.476775i	$-0.841806\pi$
$941$	−12.3393	+	12.3393i	−0.402251	+	0.402251i	0.476775	+	0.879026i	$0.341806\pi$
$942$		0			0
$943$	−2.43228	−	2.43228i	−0.0792060	−	0.0792060i
$944$	−25.3538	+	21.8330i	−0.825194	+	0.710604i
$945$		0			0
$946$	16.8015	−	38.5181i	0.546265	−	1.25233i
$947$			48.3611i			1.57152i	0.618529	+	0.785762i	$0.287729\pi$
$947$			48.3611i			1.57152i	−0.618529	+	0.785762i	$0.712271\pi$
$948$		0			0
$949$	−2.03807	+	2.03807i	−0.0661585	+	0.0661585i
$950$	−34.5979	+	13.0442i	−1.12250	+	0.423208i
$951$		0			0
$952$	14.6897	−	30.5224i	0.476095	−	0.989237i
$953$	34.0371	+	34.0371i	1.10257	+	1.10257i	0.994100	+	0.108471i	$0.0345953\pi$
$953$	34.0371	+	34.0371i	1.10257	+	1.10257i	0.108471	+	0.994100i	$0.465405\pi$
$954$		0			0
$955$	1.54794	+	3.80980i	0.0500903	+	0.123282i
$956$	2.61375	−	2.42600i	0.0845348	−	0.0784624i
$957$		0			0
$958$	−0.262346	−	0.668286i	−0.00847600	−	0.0215913i
$959$	−11.2325			−0.362716
$960$		0			0
$961$	30.9412			0.998102
$962$	−2.35956	−	6.01063i	−0.0760753	−	0.193791i
$963$		0			0
$964$	−15.3096	+	14.2099i	−0.493090	+	0.457669i
$965$	−7.60500	+	18.0142i	−0.244814	+	0.579898i
$966$		0			0
$967$	−18.9307	−	18.9307i	−0.608770	−	0.608770i	0.333855	−	0.942625i	$-0.391651\pi$
$967$	−18.9307	−	18.9307i	−0.608770	−	0.608770i	−0.942625	+	0.333855i	$0.891651\pi$
$968$	0.265314	−	0.551273i	0.00852751	−	0.0177186i
$969$		0			0
$970$	−0.185714	+	7.31347i	−0.00596290	+	0.234821i
$971$	21.2698	−	21.2698i	0.682580	−	0.682580i	−0.278001	−	0.960581i	$-0.589672\pi$
$971$	21.2698	−	21.2698i	0.682580	−	0.682580i	0.960581	+	0.278001i	$0.0896719\pi$
$972$		0			0
$973$		−	23.4822i		−	0.752805i
$974$	20.7752	−	47.6278i	0.665681	−	1.52609i
$975$		0			0
$976$	24.6358	+	28.6085i	0.788573	+	0.915736i
$977$	−2.13884	−	2.13884i	−0.0684275	−	0.0684275i	0.672065	−	0.740492i	$-0.265408\pi$
$977$	−2.13884	−	2.13884i	−0.0684275	−	0.0684275i	−0.740492	+	0.672065i	$0.765408\pi$
$978$		0			0
$979$	−22.6911	+	22.6911i	−0.725210	+	0.725210i
$980$	−17.8385	−	8.32636i	−0.569831	−	0.265976i
$981$		0			0
$982$	6.01667	+	2.62447i	0.192000	+	0.0837501i
$983$	6.18193	−	6.18193i	0.197173	−	0.197173i	−0.601614	−	0.798787i	$-0.705475\pi$
$983$	6.18193	−	6.18193i	0.197173	−	0.197173i	0.798787	+	0.601614i	$0.205475\pi$
$984$		0			0
$985$	4.67708	+	11.5113i	0.149024	+	0.366779i
$986$	32.8301	−	12.8880i	1.04552	−	0.410436i
$987$		0			0
$988$	−14.2657	−	0.531466i	−0.453853	−	0.0169082i
$989$	−8.24447	−	8.24447i	−0.262159	−	0.262159i
$990$		0			0
$991$		−	43.4847i		−	1.38134i	−0.723172	−	0.690668i	$-0.757317\pi$
$991$		−	43.4847i		−	1.38134i	0.723172	−	0.690668i	$-0.242683\pi$
$992$	0.405002	+	1.31110i	0.0128588	+	0.0416273i
$993$		0			0
$994$	−14.0707	+	32.2576i	−0.446297	+	1.02315i
$995$	−5.86173	−	14.4269i	−0.185829	−	0.457364i
$996$		0			0
$997$		−	33.4043i		−	1.05793i	−0.848645	−	0.528963i	$-0.822581\pi$
$997$		−	33.4043i		−	1.05793i	0.848645	−	0.528963i	$-0.177419\pi$
$998$	−12.3540	−	5.38879i	−0.391059	−	0.170579i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.667.6		18
3.2	odd	2		80.2.s.b.27.4	yes	18
5.3	odd	4		720.2.bd.g.523.8		18
12.11	even	2		320.2.s.b.207.3		18
15.2	even	4		400.2.j.d.43.8		18
15.8	even	4		80.2.j.b.43.2	✓	18
15.14	odd	2		400.2.s.d.107.6		18
16.3	odd	4		720.2.bd.g.307.8		18
24.5	odd	2		640.2.s.d.287.3		18
24.11	even	2		640.2.s.c.287.7		18
48.5	odd	4		640.2.j.c.607.3		18
48.11	even	4		640.2.j.d.607.7		18
48.29	odd	4		320.2.j.b.47.7		18
48.35	even	4		80.2.j.b.67.2	yes	18
60.23	odd	4		320.2.j.b.143.3		18
60.47	odd	4		1600.2.j.d.143.7		18
60.59	even	2		1600.2.s.d.207.7		18
80.3	even	4	inner	720.2.z.g.163.6		18
120.53	even	4		640.2.j.d.543.3		18
120.83	odd	4		640.2.j.c.543.7		18
240.29	odd	4		1600.2.j.d.1007.3		18
240.53	even	4		640.2.s.c.223.7		18
240.77	even	4		1600.2.s.d.943.7		18
240.83	odd	4		80.2.s.b.3.4	yes	18
240.173	even	4		320.2.s.b.303.3		18
240.179	even	4		400.2.j.d.307.8		18
240.203	odd	4		640.2.s.d.223.3		18
240.227	odd	4		400.2.s.d.243.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.2	✓	18	15.8	even	4
80.2.j.b.67.2	yes	18	48.35	even	4
80.2.s.b.3.4	yes	18	240.83	odd	4
80.2.s.b.27.4	yes	18	3.2	odd	2
320.2.j.b.47.7		18	48.29	odd	4
320.2.j.b.143.3		18	60.23	odd	4
320.2.s.b.207.3		18	12.11	even	2
320.2.s.b.303.3		18	240.173	even	4
400.2.j.d.43.8		18	15.2	even	4
400.2.j.d.307.8		18	240.179	even	4
400.2.s.d.107.6		18	15.14	odd	2
400.2.s.d.243.6		18	240.227	odd	4
640.2.j.c.543.7		18	120.83	odd	4
640.2.j.c.607.3		18	48.5	odd	4
640.2.j.d.543.3		18	120.53	even	4
640.2.j.d.607.7		18	48.11	even	4
640.2.s.c.223.7		18	240.53	even	4
640.2.s.c.287.7		18	24.11	even	2
640.2.s.d.223.3		18	240.203	odd	4
640.2.s.d.287.3		18	24.5	odd	2
720.2.z.g.163.6		18	80.3	even	4	inner
720.2.z.g.667.6		18	1.1	even	1	trivial
720.2.bd.g.307.8		18	16.3	odd	4
720.2.bd.g.523.8		18	5.3	odd	4
1600.2.j.d.143.7		18	60.47	odd	4
1600.2.j.d.1007.3		18	240.29	odd	4
1600.2.s.d.207.7		18	60.59	even	2
1600.2.s.d.943.7		18	240.77	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.516777 + 1.31641i) q^{2} +(-1.46588 + 1.36058i) q^{4} +(-2.07160 + 0.841703i) q^{5} +(-1.13975 - 1.13975i) q^{7} +(-2.54862 - 1.22659i) q^{8} +O(q^{10})\)	\(q+(0.516777 + 1.31641i) q^{2} +(-1.46588 + 1.36058i) q^{4} +(-2.07160 + 0.841703i) q^{5} +(-1.13975 - 1.13975i) q^{7} +(-2.54862 - 1.22659i) q^{8} +(-2.17858 - 2.29211i) q^{10} +(2.32204 - 2.32204i) q^{11} -1.36502i q^{13} +(0.911384 - 2.08938i) q^{14} +(0.297625 - 3.98891i) q^{16} +(-5.25380 - 5.25380i) q^{17} +(-3.69752 + 3.69752i) q^{19} +(1.89152 - 4.05243i) q^{20} +(4.25673 + 1.85678i) q^{22} +(0.911118 - 0.911118i) q^{23} +(3.58307 - 3.48735i) q^{25} +(1.79693 - 0.705412i) q^{26} +(3.22146 + 0.120015i) q^{28} +(2.37343 + 2.37343i) q^{29} +0.242577i q^{31} +(5.40486 - 1.66958i) q^{32} +(4.20112 - 9.63121i) q^{34} +(3.32044 + 1.40178i) q^{35} -3.34494i q^{37} +(-6.77825 - 2.95666i) q^{38} +(6.31216 + 0.395820i) q^{40} -2.66956i q^{41} -9.04874i q^{43} +(-0.244509 + 6.56316i) q^{44} +(1.67025 + 0.728562i) q^{46} +(-7.87820 + 7.87820i) q^{47} -4.40194i q^{49} +(6.44244 + 2.91462i) q^{50} +(1.85723 + 2.00096i) q^{52} +5.80113 q^{53} +(-2.85587 + 6.76480i) q^{55} +(1.50679 + 4.30279i) q^{56} +(-1.89788 + 4.35095i) q^{58} +(-5.91474 - 5.91474i) q^{59} +(-6.67404 + 6.67404i) q^{61} +(-0.319332 + 0.125358i) q^{62} +(4.99096 + 6.25222i) q^{64} +(1.14894 + 2.82778i) q^{65} -4.54673i q^{67} +(14.8497 + 0.553222i) q^{68} +(-0.129391 + 5.09547i) q^{70} -15.4389 q^{71} +(-1.49307 - 1.49307i) q^{73} +(4.40332 - 1.72859i) q^{74} +(0.389347 - 10.4509i) q^{76} -5.29308 q^{77} -10.3024 q^{79} +(2.74092 + 8.51395i) q^{80} +(3.51424 - 1.37957i) q^{82} -3.26589 q^{83} +(15.3059 + 6.46165i) q^{85} +(11.9119 - 4.67618i) q^{86} +(-8.76618 + 3.06981i) q^{88} -9.77206 q^{89} +(-1.55578 + 1.55578i) q^{91} +(-0.0959403 + 2.57524i) q^{92} +(-14.4422 - 6.29969i) q^{94} +(4.54758 - 10.7720i) q^{95} +(-1.63587 - 1.63587i) q^{97} +(5.79477 - 2.27482i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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