LMFDB - Embedded newform 198.2.l.a.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(17,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("198.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.l (of order $10$, 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:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.1
Root			$-1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	198.161
Dual form			198.2.l.a.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.63178 - 2.24595i) q^{5} +(-4.12554 + 1.34047i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.63178 - 2.24595i) q^{5} +(-4.12554 + 1.34047i) q^{7} +(0.309017 - 0.951057i) q^{8} +2.77615i q^{10} +(-3.30803 + 0.238643i) q^{11} +(2.74981 - 3.78479i) q^{13} +(4.12554 + 1.34047i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.17625 + 2.30768i) q^{17} +(-4.41232 - 1.43365i) q^{19} +(1.63178 - 2.24595i) q^{20} +(2.81652 + 1.75134i) q^{22} -2.86730i q^{23} +(-0.836503 + 2.57449i) q^{25} +(-4.44929 + 1.44566i) q^{26} +(-2.54972 - 3.50939i) q^{28} +(0.977763 + 3.00925i) q^{29} +(3.90222 + 2.83513i) q^{31} +1.00000 q^{32} +3.92606 q^{34} +(9.74258 + 7.07840i) q^{35} +(-2.17625 - 6.69781i) q^{37} +(2.72696 + 3.75334i) q^{38} +(-2.64027 + 0.857876i) q^{40} +(-0.290024 + 0.892603i) q^{41} -7.98397i q^{43} +(-1.24920 - 3.07238i) q^{44} +(-1.68536 + 2.31969i) q^{46} +(5.02285 + 1.63202i) q^{47} +(9.56009 - 6.94582i) q^{49} +(2.18999 - 1.59112i) q^{50} +(4.44929 + 1.44566i) q^{52} +(7.77045 - 10.6951i) q^{53} +(5.93394 + 7.04025i) q^{55} +4.33785i q^{56} +(0.977763 - 3.00925i) q^{58} +(-4.93230 + 1.60260i) q^{59} +(5.46164 + 7.51730i) q^{61} +(-1.49052 - 4.58734i) q^{62} +(-0.809017 - 0.587785i) q^{64} -12.9875 q^{65} -2.82859 q^{67} +(-3.17625 - 2.30768i) q^{68} +(-3.72134 - 11.4531i) q^{70} +(0.944821 + 1.30043i) q^{71} +(-13.6579 + 4.43773i) q^{73} +(-2.17625 + 6.69781i) q^{74} -4.63939i q^{76} +(13.3275 - 5.41884i) q^{77} +(-5.11504 + 7.04025i) q^{79} +(2.64027 + 0.857876i) q^{80} +(0.759294 - 0.551659i) q^{82} +(-7.71124 + 5.60255i) q^{83} +(10.3659 + 3.36807i) q^{85} +(-4.69286 + 6.45917i) q^{86} +(-0.795274 + 3.21987i) q^{88} -7.05342i q^{89} +(-6.27106 + 19.3003i) q^{91} +(2.72696 - 0.886044i) q^{92} +(-3.10429 - 4.27269i) q^{94} +(3.98002 + 12.2492i) q^{95} +(-8.66213 - 6.29341i) q^{97} -11.8169 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8	$ 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8} + 4 q^{11} - 2 q^{16} - 8 q^{17} - 6 q^{22} + 6 q^{25} - 20 q^{26} - 10 q^{28} + 10 q^{29} - 14 q^{31} + 8 q^{32} - 8 q^{34} + 10 q^{35} + 20 q^{38} - 10 q^{40} - 8 q^{41} - 6 q^{44} + 20 q^{46} + 20 q^{47} + 6 q^{49} - 4 q^{50} + 20 q^{52} + 30 q^{53} + 28 q^{55} + 10 q^{58} - 20 q^{59} + 20 q^{61} + 16 q^{62} - 2 q^{64} - 64 q^{65} - 56 q^{67} - 8 q^{68} + 10 q^{70} + 20 q^{71} - 10 q^{73} - 20 q^{79} + 10 q^{80} + 12 q^{82} - 12 q^{83} + 20 q^{86} - 6 q^{88} + 20 q^{92} - 20 q^{94} + 16 q^{95} - 12 q^{97} - 44 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8 + 4 * q^11 - 2 * q^16 - 8 * q^17 - 6 * q^22 + 6 * q^25 - 20 * q^26 - 10 * q^28 + 10 * q^29 - 14 * q^31 + 8 * q^32 - 8 * q^34 + 10 * q^35 + 20 * q^38 - 10 * q^40 - 8 * q^41 - 6 * q^44 + 20 * q^46 + 20 * q^47 + 6 * q^49 - 4 * q^50 + 20 * q^52 + 30 * q^53 + 28 * q^55 + 10 * q^58 - 20 * q^59 + 20 * q^61 + 16 * q^62 - 2 * q^64 - 64 * q^65 - 56 * q^67 - 8 * q^68 + 10 * q^70 + 20 * q^71 - 10 * q^73 - 20 * q^79 + 10 * q^80 + 12 * q^82 - 12 * q^83 + 20 * q^86 - 6 * q^88 + 20 * q^92 - 20 * q^94 + 16 * q^95 - 12 * q^97 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.63178	−	2.24595i	−0.729753	−	1.00442i	−0.999143	−	0.0413876i	$-0.986822\pi$
$5$	−1.63178	−	2.24595i	−0.729753	−	1.00442i	0.269390	−	0.963031i	$-0.413178\pi$
$6$		0			0
$7$	−4.12554	+	1.34047i	−1.55931	+	0.506650i	−0.956623	−	0.291330i	$-0.905902\pi$
$7$	−4.12554	+	1.34047i	−1.55931	+	0.506650i	−0.602684	+	0.797980i	$0.705902\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$			2.77615i			0.877894i
$11$	−3.30803	+	0.238643i	−0.997408	+	0.0719536i
$11$	−3.30803	+	0.238643i	−0.997408	+	0.0719536i
$12$		0			0
$13$	2.74981	−	3.78479i	0.762660	−	1.04971i	−0.234328	−	0.972158i	$-0.575289\pi$
$13$	2.74981	−	3.78479i	0.762660	−	1.04971i	0.996988	−	0.0775543i	$-0.0247111\pi$
$14$	4.12554	+	1.34047i	1.10260	+	0.358255i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.17625	+	2.30768i	−0.770354	+	0.559695i	−0.902069	−	0.431593i	$-0.857952\pi$
$17$	−3.17625	+	2.30768i	−0.770354	+	0.559695i	0.131715	+	0.991288i	$0.457952\pi$
$18$		0			0
$19$	−4.41232	−	1.43365i	−1.01226	−	0.328902i	−0.244503	−	0.969649i	$-0.578625\pi$
$19$	−4.41232	−	1.43365i	−1.01226	−	0.328902i	−0.767752	+	0.640747i	$0.778625\pi$
$20$	1.63178	−	2.24595i	0.364876	−	0.502209i
$21$		0			0
$22$	2.81652	+	1.75134i	0.600484	+	0.373388i
$23$		−	2.86730i		−	0.597873i	−0.954273	−	0.298937i	$-0.903368\pi$
$23$		−	2.86730i		−	0.597873i	0.954273	−	0.298937i	$-0.0966319\pi$
$24$		0			0
$25$	−0.836503	+	2.57449i	−0.167301	+	0.514898i
$26$	−4.44929	+	1.44566i	−0.872577	+	0.283517i
$27$		0			0
$28$	−2.54972	−	3.50939i	−0.481852	−	0.663213i
$29$	0.977763	+	3.00925i	0.181566	+	0.558803i	0.999872	−	0.0159796i	$-0.00508668\pi$
$29$	0.977763	+	3.00925i	0.181566	+	0.558803i	−0.818306	+	0.574782i	$0.805087\pi$
$30$		0			0
$31$	3.90222	+	2.83513i	0.700860	+	0.509205i	0.880212	−	0.474580i	$-0.157400\pi$
$31$	3.90222	+	2.83513i	0.700860	+	0.509205i	−0.179352	+	0.983785i	$0.557400\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	3.92606			0.673314
$35$	9.74258	+	7.07840i	1.64680	+	1.19647i
$36$		0			0
$37$	−2.17625	−	6.69781i	−0.357773	−	1.10111i	−0.954384	−	0.298582i	$-0.903486\pi$
$37$	−2.17625	−	6.69781i	−0.357773	−	1.10111i	0.596610	−	0.802531i	$-0.296514\pi$
$38$	2.72696	+	3.75334i	0.442372	+	0.608873i
$39$		0			0
$40$	−2.64027	+	0.857876i	−0.417463	+	0.135642i
$41$	−0.290024	+	0.892603i	−0.0452942	+	0.139401i	−0.971146	−	0.238485i	$-0.923349\pi$
$41$	−0.290024	+	0.892603i	−0.0452942	+	0.139401i	0.925852	+	0.377887i	$0.123349\pi$
$42$		0			0
$43$		−	7.98397i		−	1.21754i	−0.793345	−	0.608772i	$-0.791662\pi$
$43$		−	7.98397i		−	1.21754i	0.793345	−	0.608772i	$-0.208338\pi$
$44$	−1.24920	−	3.07238i	−0.188324	−	0.463178i
$45$		0			0
$46$	−1.68536	+	2.31969i	−0.248492	+	0.342020i
$47$	5.02285	+	1.63202i	0.732658	+	0.238055i	0.651502	−	0.758647i	$-0.274139\pi$
$47$	5.02285	+	1.63202i	0.732658	+	0.238055i	0.0811553	+	0.996701i	$0.474139\pi$
$48$		0			0
$49$	9.56009	−	6.94582i	1.36573	−	0.992259i
$50$	2.18999	−	1.59112i	0.309712	−	0.225019i
$51$		0			0
$52$	4.44929	+	1.44566i	0.617005	+	0.200477i
$53$	7.77045	−	10.6951i	1.06735	−	1.46909i	0.194626	−	0.980878i	$-0.437651\pi$
$53$	7.77045	−	10.6951i	1.06735	−	1.46909i	0.872727	−	0.488208i	$-0.162349\pi$
$54$		0			0
$55$	5.93394	+	7.04025i	0.800133	+	0.949307i
$56$			4.33785i			0.579669i
$57$		0			0
$58$	0.977763	−	3.00925i	0.128387	−	0.395133i
$59$	−4.93230	+	1.60260i	−0.642131	+	0.208641i	−0.611941	−	0.790903i	$-0.709611\pi$
$59$	−4.93230	+	1.60260i	−0.642131	+	0.208641i	−0.0301896	+	0.999544i	$0.509611\pi$
$60$		0			0
$61$	5.46164	+	7.51730i	0.699291	+	0.962491i	0.999962	+	0.00876342i	$0.00278952\pi$
$61$	5.46164	+	7.51730i	0.699291	+	0.962491i	−0.300671	+	0.953728i	$0.597210\pi$
$62$	−1.49052	−	4.58734i	−0.189296	−	0.582593i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−12.9875			−1.61090
$66$		0			0
$67$	−2.82859			−0.345568			−0.172784	−	0.984960i	$-0.555276\pi$
$67$	−2.82859			−0.345568			−0.172784	+	0.984960i	$0.555276\pi$
$68$	−3.17625	−	2.30768i	−0.385177	−	0.279847i
$69$		0			0
$70$	−3.72134	−	11.4531i	−0.444785	−	1.36891i
$71$	0.944821	+	1.30043i	0.112130	+	0.154333i	0.861393	−	0.507939i	$-0.169592\pi$
$71$	0.944821	+	1.30043i	0.112130	+	0.154333i	−0.749264	+	0.662272i	$0.769592\pi$
$72$		0			0
$73$	−13.6579	+	4.43773i	−1.59854	+	0.519397i	−0.966746	−	0.255738i	$-0.917682\pi$
$73$	−13.6579	+	4.43773i	−1.59854	+	0.519397i	−0.631795	+	0.775136i	$0.717682\pi$
$74$	−2.17625	+	6.69781i	−0.252984	+	0.778605i
$75$		0			0
$76$		−	4.63939i		−	0.532174i
$77$	13.3275	−	5.41884i	1.51881	−	0.617534i
$78$		0			0
$79$	−5.11504	+	7.04025i	−0.575487	+	0.792090i	−0.993192	−	0.116493i	$-0.962835\pi$
$79$	−5.11504	+	7.04025i	−0.575487	+	0.792090i	0.417705	+	0.908583i	$0.362835\pi$
$80$	2.64027	+	0.857876i	0.295191	+	0.0959135i
$81$		0			0
$82$	0.759294	−	0.551659i	0.0838500	−	0.0609206i
$83$	−7.71124	+	5.60255i	−0.846419	+	0.614959i	−0.924156	−	0.382015i	$-0.875230\pi$
$83$	−7.71124	+	5.60255i	−0.846419	+	0.614959i	0.0777375	+	0.996974i	$0.475230\pi$
$84$		0			0
$85$	10.3659	+	3.36807i	1.12434	+	0.365319i
$86$	−4.69286	+	6.45917i	−0.506044	+	0.696510i
$87$		0			0
$88$	−0.795274	+	3.21987i	−0.0847765	+	0.343239i
$89$		−	7.05342i		−	0.747661i	−0.927497	−	0.373831i	$-0.878044\pi$
$89$		−	7.05342i		−	0.747661i	0.927497	−	0.373831i	$-0.121956\pi$
$90$		0			0
$91$	−6.27106	+	19.3003i	−0.657386	+	2.02322i
$92$	2.72696	−	0.886044i	0.284306	−	0.0923765i
$93$		0			0
$94$	−3.10429	−	4.27269i	−0.320183	−	0.440694i
$95$	3.98002	+	12.2492i	0.408341	+	1.25675i
$96$		0			0
$97$	−8.66213	−	6.29341i	−0.879506	−	0.638999i	0.0536147	−	0.998562i	$-0.482926\pi$
$97$	−8.66213	−	6.29341i	−0.879506	−	0.638999i	−0.933121	+	0.359563i	$0.882926\pi$
$98$	−11.8169			−1.19369
$99$		0			0
$100$	−2.70698			−0.270698
$101$	−7.17785	−	5.21501i	−0.714223	−	0.518913i	0.170310	−	0.985390i	$-0.445523\pi$
$101$	−7.17785	−	5.21501i	−0.714223	−	0.518913i	−0.884533	+	0.466477i	$0.845523\pi$
$102$		0			0
$103$	−0.372861	−	1.14755i	−0.0367391	−	0.113071i	0.931005	−	0.365006i	$-0.118933\pi$
$103$	−0.372861	−	1.14755i	−0.0367391	−	0.113071i	−0.967744	+	0.251935i	$0.918933\pi$
$104$	−2.74981	−	3.78479i	−0.269641	−	0.371129i
$105$		0			0
$106$	−12.5728	+	4.08517i	−1.22118	+	0.396786i
$107$	2.53984	−	7.81681i	0.245535	−	0.755680i	−0.750013	−	0.661423i	$-0.769953\pi$
$107$	2.53984	−	7.81681i	0.245535	−	0.755680i	0.995548	−	0.0942562i	$-0.0300473\pi$
$108$		0			0
$109$		−	1.78973i		−	0.171425i	−0.996320	−	0.0857127i	$-0.972683\pi$
$109$		−	1.78973i		−	0.171425i	0.996320	−	0.0857127i	$-0.0273167\pi$
$110$	−0.662508	−	9.18357i	−0.0631676	−	0.875619i
$111$		0			0
$112$	2.54972	−	3.50939i	0.240926	−	0.331606i
$113$	−13.7446	−	4.46590i	−1.29299	−	0.420117i	−0.419850	−	0.907593i	$-0.637917\pi$
$113$	−13.7446	−	4.46590i	−1.29299	−	0.420117i	−0.873136	+	0.487477i	$0.837917\pi$
$114$		0			0
$115$	−6.43981	+	4.67879i	−0.600515	+	0.436300i
$116$	−2.55982	+	1.85982i	−0.237673	+	0.172680i
$117$		0			0
$118$	4.93230	+	1.60260i	0.454055	+	0.147531i
$119$	10.0104	−	13.7781i	0.917649	−	1.26304i
$120$		0			0
$121$	10.8861	−	1.57888i	0.989645	−	0.143534i
$122$		−	9.29189i		−	0.841248i
$123$		0			0
$124$	−1.49052	+	4.58734i	−0.133852	+	0.411955i
$125$	−6.05419	+	1.96713i	−0.541503	+	0.175945i
$126$		0			0
$127$	−7.04250	−	9.69316i	−0.624920	−	0.860129i	0.372779	−	0.927920i	$-0.378405\pi$
$127$	−7.04250	−	9.69316i	−0.624920	−	0.860129i	−0.997700	+	0.0677909i	$0.978405\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	10.5071	+	7.63387i	0.921536	+	0.669535i
$131$	4.03478			0.352521			0.176260	−	0.984344i	$-0.443600\pi$
$131$	4.03478			0.352521			0.176260	+	0.984344i	$0.443600\pi$
$132$		0			0
$133$	20.1250			1.74505
$134$	2.28838	+	1.66261i	0.197686	+	0.143627i
$135$		0			0
$136$	1.21322	+	3.73391i	0.104033	+	0.320180i
$137$	6.50324	+	8.95095i	0.555610	+	0.764731i	0.990760	−	0.135627i	$-0.0433048\pi$
$137$	6.50324	+	8.95095i	0.555610	+	0.764731i	−0.435150	+	0.900358i	$0.643305\pi$
$138$		0			0
$139$	3.33749	−	1.08442i	0.283082	−	0.0919790i	−0.164034	−	0.986455i	$-0.552451\pi$
$139$	3.33749	−	1.08442i	0.283082	−	0.0919790i	0.447117	+	0.894476i	$0.352451\pi$
$140$	−3.72134	+	11.4531i	−0.314510	+	0.967963i
$141$		0			0
$142$		−	1.60743i		−	0.134892i
$143$	−8.19324	+	13.1764i	−0.685153	+	1.10187i
$144$		0			0
$145$	5.16312	−	7.10642i	0.428774	−	0.590156i
$146$	13.6579	+	4.43773i	1.13034	+	0.367269i
$147$		0			0
$148$	5.69750	−	4.13948i	0.468332	−	0.340263i
$149$	1.03598	−	0.752684i	0.0848708	−	0.0616622i	−0.544541	−	0.838734i	$-0.683296\pi$
$149$	1.03598	−	0.752684i	0.0848708	−	0.0616622i	0.629411	+	0.777072i	$0.283296\pi$
$150$		0			0
$151$	−13.9570	−	4.53491i	−1.13581	−	0.369046i	−0.320027	−	0.947408i	$-0.603692\pi$
$151$	−13.9570	−	4.53491i	−1.13581	−	0.369046i	−0.815780	+	0.578363i	$0.803692\pi$
$152$	−2.72696	+	3.75334i	−0.221186	+	0.304436i
$153$		0			0
$154$	−13.9673	−	3.44978i	−1.12552	−	0.277991i
$155$		−	13.3905i		−	1.07555i
$156$		0			0
$157$	−6.63966	+	20.4348i	−0.529903	+	1.63087i	0.224510	+	0.974472i	$0.427922\pi$
$157$	−6.63966	+	20.4348i	−0.529903	+	1.63087i	−0.754413	+	0.656401i	$0.772078\pi$
$158$	8.27631	−	2.68914i	0.658428	−	0.213936i
$159$		0			0
$160$	−1.63178	−	2.24595i	−0.129003	−	0.177558i
$161$	3.84352	+	11.8292i	0.302912	+	0.932268i
$162$		0			0
$163$	8.82928	+	6.41484i	0.691562	+	0.502449i	0.877173	−	0.480174i	$-0.159426\pi$
$163$	8.82928	+	6.41484i	0.691562	+	0.502449i	−0.185611	+	0.982623i	$0.559426\pi$
$164$	−0.938539			−0.0732876
$165$		0			0
$166$	9.53162			0.739797
$167$	−5.28320	−	3.83847i	−0.408826	−	0.297030i	0.364300	−	0.931282i	$-0.381308\pi$
$167$	−5.28320	−	3.83847i	−0.408826	−	0.297030i	−0.773127	+	0.634252i	$0.781308\pi$
$168$		0			0
$169$	−2.74596	−	8.45118i	−0.211227	−	0.650091i
$170$	−6.40646	−	8.81773i	−0.491353	−	0.676289i
$171$		0			0
$172$	7.59321	−	2.46718i	0.578977	−	0.188121i
$173$	2.20985	−	6.80121i	0.168012	−	0.517087i	−0.831234	−	0.555923i	$-0.812365\pi$
$173$	2.20985	−	6.80121i	0.168012	−	0.517087i	0.999246	+	0.0388361i	$0.0123650\pi$
$174$		0			0
$175$		−	11.7425i		−	0.887648i
$176$	2.53598	−	2.13748i	0.191157	−	0.161118i
$177$		0			0
$178$	−4.14590	+	5.70634i	−0.310748	+	0.427708i
$179$	20.0813	+	6.52481i	1.50095	+	0.487687i	0.940294	−	0.340364i	$-0.110550\pi$
$179$	20.0813	+	6.52481i	1.50095	+	0.487687i	0.560653	+	0.828051i	$0.310550\pi$
$180$		0			0
$181$	3.90321	−	2.83585i	0.290124	−	0.210787i	−0.433197	−	0.901299i	$-0.642615\pi$
$181$	3.90321	−	2.83585i	0.290124	−	0.210787i	0.723321	+	0.690512i	$0.242615\pi$
$182$	16.4178	−	11.9283i	1.21697	−	0.884182i
$183$		0			0
$184$	−2.72696	−	0.886044i	−0.201034	−	0.0653200i
$185$	−11.4918	+	15.8171i	−0.844893	+	1.16290i
$186$		0			0
$187$	9.95641	−	8.39186i	0.728085	−	0.613674i
$188$			5.28134i			0.385181i
$189$		0			0
$190$	3.98002	−	12.2492i	0.288741	−	0.888653i
$191$	−10.4768	+	3.40411i	−0.758073	+	0.246313i	−0.662451	−	0.749105i	$-0.730484\pi$
$191$	−10.4768	+	3.40411i	−0.758073	+	0.246313i	−0.0956215	+	0.995418i	$0.530484\pi$
$192$		0			0
$193$	−11.7974	−	16.2377i	−0.849194	−	1.16882i	−0.984040	−	0.177949i	$-0.943054\pi$
$193$	−11.7974	−	16.2377i	−0.849194	−	1.16882i	0.134845	−	0.990867i	$-0.456946\pi$
$194$	3.30864	+	10.1829i	0.237546	+	0.731093i
$195$		0			0
$196$	9.56009	+	6.94582i	0.682864	+	0.496130i
$197$	20.3962			1.45317			0.726585	−	0.687076i	$-0.241106\pi$
$197$	20.3962			1.45317			0.726585	+	0.687076i	$0.241106\pi$
$198$		0			0
$199$	5.89735			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$199$	5.89735			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$200$	2.18999	+	1.59112i	0.154856	+	0.112509i
$201$		0			0
$202$	2.74170	+	8.43807i	0.192905	+	0.593701i
$203$	−8.06760	−	11.1041i	−0.566234	−	0.779355i
$204$		0			0
$205$	2.47800	−	0.805150i	0.173071	−	0.0562341i
$206$	−0.372861	+	1.14755i	−0.0259785	+	0.0799535i
$207$		0			0
$208$			4.67826i			0.324379i
$209$	14.9382	+	3.68958i	1.03330	+	0.255214i
$210$		0			0
$211$	3.91270	−	5.38536i	0.269361	−	0.370744i	−0.652813	−	0.757519i	$-0.726411\pi$
$211$	3.91270	−	5.38536i	0.269361	−	0.370744i	0.922174	+	0.386775i	$0.126411\pi$
$212$	12.5728	+	4.08517i	0.863507	+	0.280570i
$213$		0			0
$214$	−6.64938	+	4.83105i	−0.454542	+	0.330244i
$215$	−17.9316	+	13.0281i	−1.22292	+	0.888506i
$216$		0			0
$217$	−19.8992	−	6.46564i	−1.35084	−	0.438916i
$218$	−1.05198	+	1.44792i	−0.0712490	+	0.0980658i
$219$		0			0
$220$	−4.86198	+	7.81907i	−0.327795	+	0.527162i
$221$			18.3671i			1.23551i
$222$		0			0
$223$	6.73795	−	20.7373i	0.451206	−	1.38867i	−0.424326	−	0.905510i	$-0.639489\pi$
$223$	6.73795	−	20.7373i	0.451206	−	1.38867i	0.875532	−	0.483160i	$-0.160511\pi$
$224$	−4.12554	+	1.34047i	−0.275649	+	0.0895638i
$225$		0			0
$226$	8.49465	+	11.6919i	0.565056	+	0.777732i
$227$	−0.755816	−	2.32616i	−0.0501653	−	0.154393i	0.922836	−	0.385194i	$-0.125865\pi$
$227$	−0.755816	−	2.32616i	−0.0501653	−	0.154393i	−0.973001	+	0.230801i	$0.925865\pi$
$228$		0			0
$229$	−5.74197	−	4.17179i	−0.379440	−	0.275679i	0.381674	−	0.924297i	$-0.375348\pi$
$229$	−5.74197	−	4.17179i	−0.379440	−	0.275679i	−0.761115	+	0.648617i	$0.775348\pi$
$230$	7.96004			0.524869
$231$		0			0
$232$	3.16411			0.207734
$233$	13.9411	+	10.1288i	0.913310	+	0.663559i	0.941850	−	0.336034i	$-0.109086\pi$
$233$	13.9411	+	10.1288i	0.913310	+	0.663559i	−0.0285398	+	0.999593i	$0.509086\pi$
$234$		0			0
$235$	−4.53073	−	13.9442i	−0.295552	−	0.909616i
$236$	−3.04833	−	4.19567i	−0.198429	−	0.273115i
$237$		0			0
$238$	−16.1971	+	5.26276i	−1.04990	+	0.341134i
$239$	5.99802	−	18.4600i	0.387980	−	1.19408i	−0.546316	−	0.837579i	$-0.683970\pi$
$239$	5.99802	−	18.4600i	0.387980	−	1.19408i	0.934295	−	0.356500i	$-0.116030\pi$
$240$		0			0
$241$			13.5085i			0.870157i	0.900392	+	0.435079i	$0.143279\pi$
$241$			13.5085i			0.870157i	−0.900392	+	0.435079i	$0.856721\pi$
$242$	−9.73508	−	5.12135i	−0.625795	−	0.329213i
$243$		0			0
$244$	−5.46164	+	7.51730i	−0.349645	+	0.481246i
$245$	−31.1999	−	10.1375i	−1.99329	−	0.647658i
$246$		0			0
$247$	−17.5591	+	12.7574i	−1.11726	+	0.811736i
$248$	3.90222	−	2.83513i	0.247792	−	0.180031i
$249$		0			0
$250$	6.05419	+	1.96713i	0.382901	+	0.124412i
$251$	−10.1389	+	13.9550i	−0.639962	+	0.880832i	−0.998614	−	0.0526394i	$-0.983237\pi$
$251$	−10.1389	+	13.9550i	−0.639962	+	0.880832i	0.358652	+	0.933471i	$0.383237\pi$
$252$		0			0
$253$	0.684261	+	9.48510i	0.0430191	+	0.596323i
$254$			11.9814i			0.751780i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.92750	+	0.951202i	−0.182612	+	0.0593344i	−0.398896	−	0.916996i	$-0.630606\pi$
$257$	−2.92750	+	0.951202i	−0.182612	+	0.0593344i	0.216283	+	0.976331i	$0.430606\pi$
$258$		0			0
$259$	17.9564	+	24.7149i	1.11576	+	1.53571i
$260$	−4.01337	−	12.3519i	−0.248898	−	0.766030i
$261$		0			0
$262$	−3.26421	−	2.37159i	−0.201664	−	0.146517i
$263$	12.1040			0.746362			0.373181	−	0.927759i	$-0.378267\pi$
$263$	12.1040			0.746362			0.373181	+	0.927759i	$0.378267\pi$
$264$		0			0
$265$	−36.7003			−2.25448
$266$	−16.2814	−	11.8292i	−0.998279	−	0.725292i
$267$		0			0
$268$	−0.874083	−	2.69015i	−0.0533931	−	0.164327i
$269$	−12.6285	−	17.3817i	−0.769975	−	1.05978i	−0.996318	−	0.0857323i	$-0.972677\pi$
$269$	−12.6285	−	17.3817i	−0.769975	−	1.05978i	0.226343	−	0.974048i	$-0.427323\pi$
$270$		0			0
$271$	25.5328	−	8.29612i	1.55101	−	0.503954i	0.596622	−	0.802523i	$-0.296509\pi$
$271$	25.5328	−	8.29612i	1.55101	−	0.503954i	0.954388	+	0.298569i	$0.0965093\pi$
$272$	1.21322	−	3.73391i	0.0735623	−	0.226401i
$273$		0			0
$274$		−	11.0640i		−	0.668399i
$275$	2.15279	−	8.71612i	0.129818	−	0.525602i
$276$		0			0
$277$	0.113567	−	0.156312i	0.00682359	−	0.00939187i	−0.805592	−	0.592471i	$-0.798152\pi$
$277$	0.113567	−	0.156312i	0.00682359	−	0.00939187i	0.812415	+	0.583079i	$0.198152\pi$
$278$	−3.33749	−	1.08442i	−0.200169	−	0.0650390i
$279$		0			0
$280$	9.74258	−	7.07840i	0.582231	−	0.423015i
$281$	7.47964	−	5.43428i	0.446198	−	0.324182i	−0.341895	−	0.939738i	$-0.611069\pi$
$281$	7.47964	−	5.43428i	0.446198	−	0.324182i	0.788093	+	0.615556i	$0.211069\pi$
$282$		0			0
$283$	13.5871	+	4.41473i	0.807671	+	0.262428i	0.683611	−	0.729846i	$-0.260408\pi$
$283$	13.5871	+	4.41473i	0.807671	+	0.262428i	0.124060	+	0.992275i	$0.460408\pi$
$284$	−0.944821	+	1.30043i	−0.0560648	+	0.0771666i
$285$		0			0
$286$	14.3734	−	5.84408i	0.849915	−	0.345568i
$287$		−	4.07124i		−	0.240318i
$288$		0			0
$289$	−0.490112	+	1.50841i	−0.0288301	+	0.0887300i
$290$	−8.35410	+	2.71441i	−0.490570	+	0.159396i
$291$		0			0
$292$	−8.44107	−	11.6181i	−0.493976	−	0.679900i
$293$	2.19286	+	6.74893i	0.128108	+	0.394277i	0.994455	−	0.105167i	$-0.0335377\pi$
$293$	2.19286	+	6.74893i	0.128108	+	0.394277i	−0.866346	+	0.499444i	$0.833538\pi$
$294$		0			0
$295$	11.6478	+	8.46260i	0.678160	+	0.492712i
$296$	−7.04250			−0.409337
$297$		0			0
$298$	−1.28054			−0.0741798
$299$	−10.8521	−	7.88453i	−0.627595	−	0.455974i
$300$		0			0
$301$	10.7023	+	32.9382i	0.616868	+	1.89853i
$302$	8.62592	+	11.8726i	0.496366	+	0.683189i
$303$		0			0
$304$	4.41232	−	1.43365i	0.253064	−	0.0822254i
$305$	7.97129	−	24.5331i	0.456435	−	1.40476i
$306$		0			0
$307$		−	14.4167i		−	0.822803i	−0.911454	−	0.411401i	$-0.865039\pi$
$307$		−	14.4167i		−	0.822803i	0.911454	−	0.411401i	$-0.134961\pi$
$308$	9.27205	+	11.0007i	0.528324	+	0.626823i
$309$		0			0
$310$	−7.87074	+	10.8331i	−0.447028	+	0.615281i
$311$	−30.2002	−	9.81264i	−1.71250	−	0.556424i	−0.721750	−	0.692154i	$-0.756662\pi$
$311$	−30.2002	−	9.81264i	−1.71250	−	0.556424i	−0.990746	+	0.135730i	$0.956662\pi$
$312$		0			0
$313$	−5.23447	+	3.80306i	−0.295870	+	0.214962i	−0.725810	−	0.687896i	$-0.758535\pi$
$313$	−5.23447	+	3.80306i	−0.295870	+	0.214962i	0.429940	+	0.902857i	$0.358535\pi$
$314$	17.3829	−	12.6294i	0.980971	−	0.712717i
$315$		0			0
$316$	−8.27631	−	2.68914i	−0.465579	−	0.151276i
$317$	3.55181	−	4.88864i	0.199489	−	0.274574i	−0.697539	−	0.716547i	$-0.745721\pi$
$317$	3.55181	−	4.88864i	0.199489	−	0.274574i	0.897028	+	0.441974i	$0.145721\pi$
$318$		0			0
$319$	−3.95260	−	9.72133i	−0.221303	−	0.544290i
$320$			2.77615i			0.155191i
$321$		0			0
$322$	3.84352	−	11.8292i	0.214191	−	0.659213i
$323$	17.3230	−	5.62860i	0.963880	−	0.313183i
$324$		0			0
$325$	7.44369	+	10.2454i	0.412902	+	0.568310i
$326$	−3.37248	−	10.3794i	−0.186785	−	0.574864i
$327$		0			0
$328$	0.759294	+	0.551659i	0.0419250	+	0.0304603i
$329$	−22.9096			−1.26305
$330$		0			0
$331$	−31.1275			−1.71092			−0.855461	−	0.517868i	$-0.826726\pi$
$331$	−31.1275			−1.71092			−0.855461	+	0.517868i	$0.826726\pi$
$332$	−7.71124	−	5.60255i	−0.423209	−	0.307480i
$333$		0			0
$334$	2.01800	+	6.21078i	0.110420	+	0.339839i
$335$	4.61563	+	6.35288i	0.252179	+	0.347095i
$336$		0			0
$337$	2.83842	−	0.922260i	0.154619	−	0.0502387i	−0.230685	−	0.973029i	$-0.574097\pi$
$337$	2.83842	−	0.922260i	0.154619	−	0.0502387i	0.385304	+	0.922790i	$0.374097\pi$
$338$	−2.74596	+	8.45118i	−0.149360	+	0.459684i
$339$		0			0
$340$			10.8993i			0.591098i
$341$	−13.5853	−	8.44746i	−0.735683	−	0.457456i
$342$		0			0
$343$	−12.2818	+	16.9045i	−0.663156	+	0.912757i
$344$	−7.59321	−	2.46718i	−0.409398	−	0.133022i
$345$		0			0
$346$	−5.78546	+	4.20338i	−0.311028	+	0.225975i
$347$	0.0777935	−	0.0565203i	0.00417617	−	0.00303417i	−0.585695	−	0.810531i	$-0.699178\pi$
$347$	0.0777935	−	0.0565203i	0.00417617	−	0.00303417i	0.589871	+	0.807497i	$0.299178\pi$
$348$		0			0
$349$	−2.11213	−	0.686272i	−0.113060	−	0.0367353i	0.251941	−	0.967743i	$-0.418931\pi$
$349$	−2.11213	−	0.686272i	−0.113060	−	0.0367353i	−0.365000	+	0.931007i	$0.618931\pi$
$350$	−6.90205	+	9.49986i	−0.368930	+	0.507789i
$351$		0			0
$352$	−3.30803	+	0.238643i	−0.176318	+	0.0127197i
$353$			4.56337i			0.242884i	0.992599	+	0.121442i	$0.0387518\pi$
$353$			4.56337i			0.242884i	−0.992599	+	0.121442i	$0.961248\pi$
$354$		0			0
$355$	1.37897	−	4.24404i	0.0731882	−	0.225250i
$356$	6.70820	−	2.17963i	0.355534	−	0.115520i
$357$		0			0
$358$	−12.4109	−	17.0822i	−0.655938	−	0.902821i
$359$	−0.896932	−	2.76047i	−0.0473382	−	0.145692i	0.924593	−	0.380955i	$-0.124405\pi$
$359$	−0.896932	−	2.76047i	−0.0473382	−	0.145692i	−0.971932	+	0.235263i	$0.924405\pi$
$360$		0			0
$361$	2.04188	+	1.48352i	0.107468	+	0.0780798i
$362$	−4.82464			−0.253577
$363$		0			0
$364$	−20.2936			−1.06367
$365$	32.2536	+	23.4336i	1.68823	+	1.22657i
$366$		0			0
$367$	1.35598	+	4.17328i	0.0707816	+	0.217843i	0.980189	−	0.198062i	$-0.0634648\pi$
$367$	1.35598	+	4.17328i	0.0707816	+	0.217843i	−0.909408	+	0.415905i	$0.863465\pi$
$368$	1.68536	+	2.31969i	0.0878552	+	0.120922i
$369$		0			0
$370$	18.5941	−	6.04159i	0.966661	−	0.314087i
$371$	−17.7208	+	54.5391i	−0.920020	+	2.83153i
$372$		0			0
$373$			20.7635i			1.07509i	0.843234	+	0.537547i	$0.180649\pi$
$373$			20.7635i			1.07509i	−0.843234	+	0.537547i	$0.819351\pi$
$374$	−12.9875	+	0.936927i	−0.671569	+	0.0484474i
$375$		0			0
$376$	3.10429	−	4.27269i	0.160092	−	0.220347i
$377$	14.0780	+	4.57423i	0.725055	+	0.235585i
$378$		0			0
$379$	15.8198	−	11.4938i	0.812608	−	0.590394i	−0.101977	−	0.994787i	$-0.532517\pi$
$379$	15.8198	−	11.4938i	0.812608	−	0.590394i	0.914586	+	0.404392i	$0.132517\pi$
$380$	−10.4198	+	7.57045i	−0.534526	+	0.388356i
$381$		0			0
$382$	10.4768	+	3.40411i	0.536038	+	0.174169i
$383$	15.6491	−	21.5391i	0.799630	−	1.10060i	−0.193211	−	0.981157i	$-0.561890\pi$
$383$	15.6491	−	21.5391i	0.799630	−	1.10060i	0.992842	−	0.119439i	$-0.0381097\pi$
$384$		0			0
$385$	−33.9180	−	21.0906i	−1.72862	−	1.07487i
$386$			20.0709i			1.02158i
$387$		0			0
$388$	3.30864	−	10.1829i	0.167971	−	0.516961i
$389$	20.4257	−	6.63671i	1.03562	−	0.336494i	0.258612	−	0.965981i	$-0.416735\pi$
$389$	20.4257	−	6.63671i	1.03562	−	0.336494i	0.777011	+	0.629487i	$0.216735\pi$
$390$		0			0
$391$	6.61681	+	9.10726i	0.334627	+	0.460574i
$392$	−3.65163	−	11.2386i	−0.184435	−	0.567633i
$393$		0			0
$394$	−16.5009	−	11.9886i	−0.831303	−	0.603977i
$395$	24.1586			1.21555
$396$		0			0
$397$	27.4464			1.37750			0.688748	−	0.725000i	$-0.258160\pi$
$397$	27.4464			1.37750			0.688748	+	0.725000i	$0.258160\pi$
$398$	−4.77106	−	3.46638i	−0.239152	−	0.173754i
$399$		0			0
$400$	−0.836503	−	2.57449i	−0.0418252	−	0.128725i
$401$	18.7470	+	25.8030i	0.936178	+	1.28854i	0.957400	+	0.288764i	$0.0932442\pi$
$401$	18.7470	+	25.8030i	0.936178	+	1.28854i	−0.0212224	+	0.999775i	$0.506756\pi$
$402$		0			0
$403$	21.4608	−	6.97302i	1.06904	−	0.347351i
$404$	2.74170	−	8.43807i	0.136404	−	0.419810i
$405$		0			0
$406$			13.7254i			0.681181i
$407$	8.79749	+	21.6372i	0.436075	+	1.07252i
$408$		0			0
$409$	11.5797	−	15.9380i	0.572578	−	0.788086i	−0.420279	−	0.907395i	$-0.638068\pi$
$409$	11.5797	−	15.9380i	0.572578	−	0.788086i	0.992857	+	0.119309i	$0.0380679\pi$
$410$	−2.47800	−	0.805150i	−0.122380	−	0.0397635i
$411$		0			0
$412$	0.976163	−	0.709224i	0.0480921	−	0.0349410i
$413$	18.2002	−	13.2232i	0.895571	−	0.650671i
$414$		0			0
$415$	25.1661	+	8.17695i	1.23535	+	0.401391i
$416$	2.74981	−	3.78479i	0.134821	−	0.185565i
$417$		0			0
$418$	−9.91658	−	11.7654i	−0.485036	−	0.575464i
$419$		−	23.6922i		−	1.15744i	−0.815527	−	0.578719i	$-0.803553\pi$
$419$		−	23.6922i		−	1.15744i	0.815527	−	0.578719i	$-0.196447\pi$
$420$		0			0
$421$	−0.538569	+	1.65755i	−0.0262483	+	0.0807838i	−0.963323	−	0.268346i	$-0.913523\pi$
$421$	−0.538569	+	1.65755i	−0.0262483	+	0.0807838i	0.937074	+	0.349130i	$0.113523\pi$
$422$	−6.33088	+	2.05703i	−0.308182	+	0.100134i
$423$		0			0
$424$	−7.77045	−	10.6951i	−0.377366	−	0.519400i
$425$	−3.28416	−	10.1076i	−0.159305	−	0.490291i
$426$		0			0
$427$	−32.6089	−	23.6918i	−1.57806	−	1.14652i
$428$	8.21908			0.397284
$429$		0			0
$430$	22.1647			1.06887
$431$	−20.7671	−	15.0882i	−1.00032	−	0.726774i	−0.0381619	−	0.999272i	$-0.512150\pi$
$431$	−20.7671	−	15.0882i	−1.00032	−	0.726774i	−0.962156	+	0.272498i	$0.912150\pi$
$432$		0			0
$433$	0.740579	+	2.27927i	0.0355899	+	0.109535i	0.967273	−	0.253737i	$-0.0816597\pi$
$433$	0.740579	+	2.27927i	0.0355899	+	0.109535i	−0.931683	+	0.363271i	$0.881660\pi$
$434$	12.2984	+	16.9273i	0.590341	+	0.812534i
$435$		0			0
$436$	1.70214	−	0.553058i	0.0815176	−	0.0264867i
$437$	−4.11070	+	12.6514i	−0.196641	+	0.605200i
$438$		0			0
$439$			14.2116i			0.678282i	0.940736	+	0.339141i	$0.110136\pi$
$439$			14.2116i			0.678282i	−0.940736	+	0.339141i	$0.889864\pi$
$440$	8.52936	−	3.46796i	0.406621	−	0.165329i
$441$		0			0
$442$	10.7959	−	14.8593i	0.513510	−	0.706786i
$443$	−17.6882	−	5.74724i	−0.840391	−	0.273059i	−0.142975	−	0.989726i	$-0.545667\pi$
$443$	−17.6882	−	5.74724i	−0.840391	−	0.273059i	−0.697416	+	0.716667i	$0.745667\pi$
$444$		0			0
$445$	−15.8416	+	11.5096i	−0.750965	+	0.545608i
$446$	−17.6402	+	12.8163i	−0.835286	+	0.606871i
$447$		0			0
$448$	4.12554	+	1.34047i	0.194913	+	0.0633312i
$449$	−16.4821	+	22.6856i	−0.777838	+	1.07060i	0.217679	+	0.976020i	$0.430151\pi$
$449$	−16.4821	+	22.6856i	−0.777838	+	1.07060i	−0.995517	+	0.0945814i	$0.969849\pi$
$450$		0			0
$451$	0.746395	−	3.02197i	0.0351464	−	0.142299i
$452$		−	14.4520i		−	0.679763i
$453$		0			0
$454$	−0.755816	+	2.32616i	−0.0354722	+	0.109172i
$455$	53.5805	−	17.4094i	2.51189	−	0.816164i
$456$		0			0
$457$	7.84404	+	10.7964i	0.366928	+	0.505034i	0.952063	−	0.305903i	$-0.0989582\pi$
$457$	7.84404	+	10.7964i	0.366928	+	0.505034i	−0.585134	+	0.810936i	$0.698958\pi$
$458$	2.19324	+	6.75009i	0.102483	+	0.315411i
$459$		0			0
$460$	−6.43981	−	4.67879i	−0.300257	−	0.218150i
$461$	9.73071			0.453204			0.226602	−	0.973987i	$-0.427238\pi$
$461$	9.73071			0.453204			0.226602	+	0.973987i	$0.427238\pi$
$462$		0			0
$463$	7.02626			0.326538			0.163269	−	0.986582i	$-0.447796\pi$
$463$	7.02626			0.326538			0.163269	+	0.986582i	$0.447796\pi$
$464$	−2.55982	−	1.85982i	−0.118837	−	0.0863398i
$465$		0			0
$466$	−5.32502	−	16.3887i	−0.246677	−	0.759192i
$467$	−5.59795	−	7.70491i	−0.259042	−	0.356541i	0.659610	−	0.751608i	$-0.270721\pi$
$467$	−5.59795	−	7.70491i	−0.259042	−	0.356541i	−0.918652	+	0.395067i	$0.870721\pi$
$468$		0			0
$469$	11.6695	−	3.79164i	0.538846	−	0.175082i
$470$	−4.53073	+	13.9442i	−0.208987	+	0.643196i
$471$		0			0
$472$			5.18613i			0.238711i
$473$	1.90532	+	26.4112i	0.0876067	+	1.21439i
$474$		0			0
$475$	7.38184	−	10.1602i	0.338702	−	0.466183i
$476$	16.1971	+	5.26276i	0.742394	+	0.241218i
$477$		0			0
$478$	−15.7030	+	11.4089i	−0.718240	+	0.521832i
$479$	−6.89824	+	5.01187i	−0.315189	+	0.228998i	−0.734120	−	0.679020i	$-0.762405\pi$
$479$	−6.89824	+	5.01187i	−0.315189	+	0.228998i	0.418931	+	0.908018i	$0.362405\pi$
$480$		0			0
$481$	−31.3341	−	10.1811i	−1.42871	−	0.464217i
$482$	7.94008	−	10.9286i	0.361661	−	0.497783i
$483$		0			0
$484$	4.86559	+	9.86540i	0.221163	+	0.448427i
$485$			29.7241i			1.34970i
$486$		0			0
$487$	4.86599	−	14.9760i	0.220499	−	0.678627i	−0.778218	−	0.627994i	$-0.783876\pi$
$487$	4.86599	−	14.9760i	0.220499	−	0.678627i	0.998717	−	0.0506328i	$-0.0161238\pi$
$488$	8.83711	−	2.87135i	0.400037	−	0.129980i
$489$		0			0
$490$	19.2826	+	26.5402i	0.871099	+	1.19896i
$491$	−12.8057	−	39.4118i	−0.577912	−	1.77863i	−0.626043	−	0.779789i	$-0.715326\pi$
$491$	−12.8057	−	39.4118i	−0.577912	−	1.77863i	0.0481306	−	0.998841i	$-0.484674\pi$
$492$		0			0
$493$	−10.0500	−	7.30175i	−0.452629	−	0.328854i
$494$	21.7042			0.976520
$495$		0			0
$496$	−4.82342			−0.216578
$497$	−5.64109	−	4.09849i	−0.253037	−	0.183842i
$498$		0			0
$499$	8.39596	+	25.8401i	0.375855	+	1.15676i	0.942900	+	0.333075i	$0.108086\pi$
$499$	8.39596	+	25.8401i	0.375855	+	1.15676i	−0.567045	+	0.823687i	$0.691914\pi$
$500$	−3.74170	−	5.15000i	−0.167334	−	0.230315i
$501$		0			0
$502$	16.4051	−	5.33034i	0.732195	−	0.237905i
$503$	3.11492	−	9.58673i	0.138887	−	0.427451i	−0.857287	−	0.514839i	$-0.827852\pi$
$503$	3.11492	−	9.58673i	0.138887	−	0.427451i	0.996174	+	0.0873875i	$0.0278518\pi$
$504$		0			0
$505$			24.6308i			1.09606i
$506$	5.02163	−	8.07581i	0.223238	−	0.359013i
$507$		0			0
$508$	7.04250	−	9.69316i	0.312460	−	0.430065i
$509$	1.21912	+	0.396118i	0.0540367	+	0.0175576i	0.335911	−	0.941894i	$-0.390956\pi$
$509$	1.21912	+	0.396118i	0.0540367	+	0.0175576i	−0.281874	+	0.959451i	$0.590956\pi$
$510$		0			0
$511$	50.3977	−	36.6161i	2.22946	−	1.61980i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	2.92750	+	0.951202i	0.129126	+	0.0419557i
$515$	−1.96891	+	2.70997i	−0.0867605	+	0.119416i
$516$		0			0
$517$	−17.0052	−	4.20011i	−0.747888	−	0.184721i
$518$		−	30.5493i		−	1.34226i
$519$		0			0
$520$	−4.01337	+	12.3519i	−0.175998	+	0.541665i
$521$	−35.6964	+	11.5985i	−1.56389	+	0.508138i	−0.957843	−	0.287292i	$-0.907245\pi$
$521$	−35.6964	+	11.5985i	−1.56389	+	0.508138i	−0.606045	+	0.795430i	$0.707245\pi$
$522$		0			0
$523$	1.87388	+	2.57917i	0.0819389	+	0.112779i	0.848019	−	0.529966i	$-0.177795\pi$
$523$	1.87388	+	2.57917i	0.0819389	+	0.112779i	−0.766080	+	0.642745i	$0.777795\pi$
$524$	1.24682	+	3.83731i	0.0544675	+	0.167634i
$525$		0			0
$526$	−9.79231	−	7.11453i	−0.426965	−	0.310208i
$527$	−18.9370			−0.824910
$528$		0			0
$529$	14.7786			0.642548
$530$	29.6912	+	21.5719i	1.28970	+	0.937023i
$531$		0			0
$532$	6.21895	+	19.1400i	0.269626	+	0.829823i
$533$	2.58080	+	3.55217i	0.111787	+	0.153862i
$534$		0			0
$535$	−21.7006	+	7.05095i	−0.938199	+	0.304839i
$536$	−0.874083	+	2.69015i	−0.0377547	+	0.116197i
$537$		0			0
$538$			21.4849i			0.926282i
$539$	−29.9675	+	25.2584i	−1.29079	+	1.08796i
$540$		0			0
$541$	4.52323	−	6.22569i	0.194469	−	0.267663i	−0.700636	−	0.713519i	$-0.747100\pi$
$541$	4.52323	−	6.22569i	0.194469	−	0.267663i	0.895105	+	0.445855i	$0.147100\pi$
$542$	−25.5328	−	8.29612i	−1.09673	−	0.356349i
$543$		0			0
$544$	−3.17625	+	2.30768i	−0.136181	+	0.0989410i
$545$	−4.01965	+	2.92045i	−0.172183	+	0.125098i
$546$		0			0
$547$	−4.27590	−	1.38933i	−0.182824	−	0.0594033i	0.216174	−	0.976355i	$-0.430642\pi$
$547$	−4.27590	−	1.38933i	−0.182824	−	0.0594033i	−0.398998	+	0.916952i	$0.630642\pi$
$548$	−6.50324	+	8.95095i	−0.277805	+	0.382366i
$549$		0			0
$550$	−6.86485	+	5.78611i	−0.292718	+	0.246721i
$551$		−	14.6795i		−	0.625369i
$552$		0			0
$553$	11.6651	−	35.9014i	0.496049	−	1.52668i
$554$	−0.183756	+	0.0597058i	−0.00780703	+	0.00253666i
$555$		0			0
$556$	2.06268	+	2.83904i	0.0874773	+	0.120402i
$557$	−13.0457	−	40.1507i	−0.552766	−	1.70124i	−0.701772	−	0.712402i	$-0.747607\pi$
$557$	−13.0457	−	40.1507i	−0.552766	−	1.70124i	0.149006	−	0.988836i	$-0.452393\pi$
$558$		0			0
$559$	−30.2177	−	21.9544i	−1.27807	−	0.928573i
$560$	−12.0425			−0.508888
$561$		0			0
$562$	−9.24534			−0.389991
$563$	−15.4734	−	11.2421i	−0.652124	−	0.473796i	0.211870	−	0.977298i	$-0.432045\pi$
$563$	−15.4734	−	11.2421i	−0.652124	−	0.473796i	−0.863994	+	0.503502i	$0.832045\pi$
$564$		0			0
$565$	12.3980	+	38.1571i	0.521587	+	1.60528i
$566$	−8.39731	−	11.5579i	−0.352965	−	0.485815i
$567$		0			0
$568$	1.52875	−	0.496722i	0.0641450	−	0.0208420i
$569$	8.65589	−	26.6401i	0.362874	−	1.11681i	−0.588428	−	0.808550i	$-0.700253\pi$
$569$	8.65589	−	26.6401i	0.362874	−	1.11681i	0.951302	−	0.308261i	$-0.0997471\pi$
$570$		0			0
$571$		−	6.27663i		−	0.262669i	−0.991338	−	0.131334i	$-0.958074\pi$
$571$		−	6.27663i		−	0.262669i	0.991338	−	0.131334i	$-0.0419262\pi$
$572$	−15.0634	−	3.72050i	−0.629831	−	0.155562i
$573$		0			0
$574$	−2.39301	+	3.29370i	−0.0998825	+	0.137476i
$575$	7.38184	+	2.39850i	0.307844	+	0.100025i
$576$		0			0
$577$	−19.2174	+	13.9623i	−0.800032	+	0.581257i	−0.910923	−	0.412575i	$-0.864629\pi$
$577$	−19.2174	+	13.9623i	−0.800032	+	0.581257i	0.110892	+	0.993833i	$0.464629\pi$
$578$	1.28313	−	0.932249i	0.0533712	−	0.0387765i
$579$		0			0
$580$	8.35410	+	2.71441i	0.346885	+	0.112710i
$581$	24.3030	−	33.4502i	1.00826	−	1.38775i
$582$		0			0
$583$	−23.1525	+	37.2341i	−0.958881	+	1.54208i
$584$			14.3608i			0.594254i
$585$		0			0
$586$	2.19286	−	6.74893i	0.0905862	−	0.278796i
$587$	−3.03970	+	0.987659i	−0.125462	+	0.0407650i	−0.371075	−	0.928603i	$-0.621011\pi$
$587$	−3.03970	+	0.987659i	−0.125462	+	0.0407650i	0.245613	+	0.969368i	$0.421011\pi$
$588$		0			0
$589$	−13.1533	−	18.1039i	−0.541971	−	0.745959i
$590$	−4.44905	−	13.6928i	−0.183165	−	0.563723i
$591$		0			0
$592$	5.69750	+	4.13948i	0.234166	+	0.170131i
$593$	−32.4485			−1.33250			−0.666251	−	0.745728i	$-0.732102\pi$
$593$	−32.4485			−1.33250			−0.666251	+	0.745728i	$0.732102\pi$
$594$		0			0
$595$	−47.2796			−1.93827
$596$	1.03598	+	0.752684i	0.0424354	+	0.0308311i
$597$		0			0
$598$	4.14514	+	12.7574i	0.169507	+	0.521690i
$599$	22.7306	+	31.2860i	0.928749	+	1.27831i	0.960346	+	0.278812i	$0.0899407\pi$
$599$	22.7306	+	31.2860i	0.928749	+	1.27831i	−0.0315969	+	0.999501i	$0.510059\pi$
$600$		0			0
$601$	6.70463	−	2.17846i	0.273487	−	0.0888614i	−0.169062	−	0.985605i	$-0.554074\pi$
$601$	6.70463	−	2.17846i	0.273487	−	0.0888614i	0.442550	+	0.896744i	$0.354074\pi$
$602$	10.7023	−	32.9382i	0.436192	−	1.34246i
$603$		0			0
$604$		−	14.6753i		−	0.597129i
$605$	−21.3098	−	21.8732i	−0.866365	−	0.889274i
$606$		0			0
$607$	−16.6376	+	22.8996i	−0.675297	+	0.929467i	−0.999866	−	0.0163951i	$-0.994781\pi$
$607$	−16.6376	+	22.8996i	−0.675297	+	0.929467i	0.324568	+	0.945862i	$0.394781\pi$
$608$	−4.41232	−	1.43365i	−0.178943	−	0.0581422i
$609$		0			0
$610$	−20.8691	+	15.1623i	−0.844966	+	0.613903i
$611$	19.9887	−	14.5227i	0.808658	−	0.587524i
$612$		0			0
$613$	−3.42548	−	1.11301i	−0.138354	−	0.0449539i	0.239022	−	0.971014i	$-0.423173\pi$
$613$	−3.42548	−	1.11301i	−0.138354	−	0.0449539i	−0.377375	+	0.926060i	$0.623173\pi$
$614$	−8.47391	+	11.6633i	−0.341979	+	0.470694i
$615$		0			0
$616$	−1.03520	−	14.3497i	−0.0417093	−	0.578167i
$617$			47.1625i			1.89869i	0.314232	+	0.949346i	$0.398253\pi$
$617$			47.1625i			1.89869i	−0.314232	+	0.949346i	$0.601747\pi$
$618$		0			0
$619$	2.30938	−	7.10753i	0.0928217	−	0.285676i	−0.893858	−	0.448350i	$-0.852012\pi$
$619$	2.30938	−	7.10753i	0.0928217	−	0.285676i	0.986680	+	0.162674i	$0.0520119\pi$
$620$	12.7351	−	4.13789i	0.511455	−	0.166182i
$621$		0			0
$622$	18.6647	+	25.6898i	0.748388	+	1.03007i
$623$	9.45489	+	29.0992i	0.378802	+	1.16583i
$624$		0			0
$625$	25.2471	+	18.3431i	1.00988	+	0.733724i
$626$	6.47016			0.258600
$627$		0			0
$628$	−21.4864			−0.857400
$629$	22.3687	+	16.2518i	0.891900	+	0.648003i
$630$		0			0
$631$	−6.12838	−	18.8612i	−0.243967	−	0.750853i	−0.995805	−	0.0915047i	$-0.970832\pi$
$631$	−6.12838	−	18.8612i	−0.243967	−	0.750853i	0.751838	−	0.659348i	$-0.229168\pi$
$632$	5.11504	+	7.04025i	0.203465	+	0.280046i
$633$		0			0
$634$	−5.74694	+	1.86730i	−0.228240	+	0.0741598i
$635$	−10.2786	+	31.6342i	−0.407892	+	1.25536i
$636$		0			0
$637$		−	55.2826i		−	2.19038i
$638$	−2.51633	+	10.1880i	−0.0996225	+	0.403347i
$639$		0			0
$640$	1.63178	−	2.24595i	0.0645017	−	0.0887789i
$641$	9.70589	+	3.15364i	0.383360	+	0.124561i	0.494356	−	0.869260i	$-0.335404\pi$
$641$	9.70589	+	3.15364i	0.383360	+	0.124561i	−0.110996	+	0.993821i	$0.535404\pi$
$642$		0			0
$643$	−33.1784	+	24.1055i	−1.30843	+	0.950628i	−1.00000		0.000620228i	$-0.999803\pi$
$643$	−33.1784	+	24.1055i	−1.30843	+	0.950628i	−0.308427	+	0.951248i	$0.599803\pi$
$644$	−10.0625	+	7.31082i	−0.396517	+	0.288087i
$645$		0			0
$646$	−17.3230	−	5.62860i	−0.681566	−	0.221454i
$647$	−26.3990	+	36.3351i	−1.03785	+	1.42848i	−0.138963	+	0.990298i	$0.544377\pi$
$647$	−26.3990	+	36.3351i	−1.03785	+	1.42848i	−0.898887	+	0.438181i	$0.855623\pi$
$648$		0			0
$649$	15.9337	−	6.47851i	0.625454	−	0.254304i
$650$		−	12.6640i		−	0.496721i
$651$		0			0
$652$	−3.37248	+	10.3794i	−0.132077	+	0.406490i
$653$	−38.0285	+	12.3562i	−1.48817	+	0.483536i	−0.936543	−	0.350554i	$-0.885993\pi$
$653$	−38.0285	+	12.3562i	−1.48817	+	0.483536i	−0.551629	+	0.834090i	$0.685993\pi$
$654$		0			0
$655$	−6.58387	−	9.06192i	−0.257253	−	0.354078i
$656$	−0.290024	−	0.892603i	−0.0113236	−	0.0348503i
$657$		0			0
$658$	18.5343	+	13.4659i	0.722541	+	0.524957i
$659$	12.3141			0.479689			0.239845	−	0.970811i	$-0.422903\pi$
$659$	12.3141			0.479689			0.239845	+	0.970811i	$0.422903\pi$
$660$		0			0
$661$	−0.190715			−0.00741794			−0.00370897	−	0.999993i	$-0.501181\pi$
$661$	−0.190715			−0.00741794			−0.00370897	+	0.999993i	$0.501181\pi$
$662$	25.1827	+	18.2963i	0.978752	+	0.711105i
$663$		0			0
$664$	2.94543	+	9.06511i	0.114305	+	0.351794i
$665$	−32.8394	−	45.1996i	−1.27346	−	1.75277i
$666$		0			0
$667$	8.62841	−	2.80354i	0.334093	−	0.108553i
$668$	2.01800	−	6.21078i	0.0780789	−	0.240302i
$669$		0			0
$670$		−	7.85259i		−	0.303372i
$671$	−19.8612	−	23.5641i	−0.766733	−	0.909680i
$672$		0			0
$673$	−3.25192	+	4.47589i	−0.125352	+	0.172533i	−0.867081	−	0.498168i	$-0.834006\pi$
$673$	−3.25192	+	4.47589i	−0.125352	+	0.172533i	0.741728	+	0.670700i	$0.234006\pi$
$674$	−2.83842	−	0.922260i	−0.109332	−	0.0355241i
$675$		0			0
$676$	7.18901	−	5.22312i	0.276500	−	0.200889i
$677$	2.10474	−	1.52918i	0.0808917	−	0.0587713i	−0.546604	−	0.837391i	$-0.684080\pi$
$677$	2.10474	−	1.52918i	0.0808917	−	0.0587713i	0.627496	+	0.778620i	$0.284080\pi$
$678$		0			0
$679$	44.1721	+	14.3524i	1.69517	+	0.550794i
$680$	6.40646	−	8.81773i	0.245676	−	0.338145i
$681$		0			0
$682$	6.02541	+	14.8193i	0.230725	+	0.567462i
$683$			1.86671i			0.0714278i	0.999362	+	0.0357139i	$0.0113705\pi$
$683$			1.86671i			0.0714278i	−0.999362	+	0.0357139i	$0.988630\pi$
$684$		0			0
$685$	9.49152	−	29.2119i	0.362652	−	1.11613i
$686$	19.8724	−	6.45694i	0.758732	−	0.246527i
$687$		0			0
$688$	4.69286	+	6.45917i	0.178914	+	0.246253i
$689$	−19.1115	−	58.8190i	−0.728089	−	2.24083i
$690$		0			0
$691$	−6.74682	−	4.90185i	−0.256661	−	0.186475i	0.452013	−	0.892011i	$-0.350706\pi$
$691$	−6.74682	−	4.90185i	−0.256661	−	0.186475i	−0.708674	+	0.705536i	$0.750706\pi$
$692$	7.15122			0.271849
$693$		0			0
$694$	−0.0961581			−0.00365011
$695$	−7.88159	−	5.72631i	−0.298966	−	0.217211i
$696$		0			0
$697$	−1.13865	−	3.50442i	−0.0431296	−	0.132739i
$698$	1.30537	+	1.79668i	0.0494089	+	0.0680055i
$699$		0			0
$700$	11.1678	−	3.62862i	0.422102	−	0.137149i
$701$	15.8509	−	48.7841i	0.598680	−	1.84255i	0.0631998	−	0.998001i	$-0.479869\pi$
$701$	15.8509	−	48.7841i	0.598680	−	1.84255i	0.535481	−	0.844548i	$-0.320131\pi$
$702$		0			0
$703$			32.6729i			1.23228i
$704$	2.81652	+	1.75134i	0.106152	+	0.0660063i
$705$		0			0
$706$	2.68228	−	3.69185i	0.100949	−	0.138944i
$707$	36.6031	+	11.8931i	1.37660	+	0.447284i
$708$		0			0
$709$	0.481952	−	0.350159i	0.0181001	−	0.0131505i	−0.578698	−	0.815542i	$-0.696439\pi$
$709$	0.481952	−	0.350159i	0.0181001	−	0.0131505i	0.596799	+	0.802391i	$0.296439\pi$
$710$	−3.61020	+	2.62296i	−0.135488	+	0.0984380i
$711$		0			0
$712$	−6.70820	−	2.17963i	−0.251401	−	0.0816850i
$713$	8.12917	−	11.1888i	0.304440	−	0.419026i
$714$		0			0
$715$	42.9631	−	3.09938i	1.60673	−	0.115910i
$716$			21.1147i			0.789094i
$717$		0			0
$718$	−0.896932	+	2.76047i	−0.0334732	+	0.103020i
$719$	−15.2023	+	4.93953i	−0.566950	+	0.184213i	−0.578446	−	0.815721i	$-0.696341\pi$
$719$	−15.2023	+	4.93953i	−0.566950	+	0.184213i	0.0114959	+	0.999934i	$0.496341\pi$
$720$		0			0
$721$	3.07651	+	4.23445i	0.114575	+	0.157699i
$722$	−0.779931	−	2.40038i	−0.0290260	−	0.0893329i
$723$		0			0
$724$	3.90321	+	2.83585i	0.145062	+	0.105394i
$725$	−8.56518			−0.318103
$726$		0			0
$727$	−17.5667			−0.651514			−0.325757	−	0.945454i	$-0.605619\pi$
$727$	−17.5667			−0.651514			−0.325757	+	0.945454i	$0.605619\pi$
$728$	16.4178	+	11.9283i	0.608486	+	0.442091i
$729$		0			0
$730$	−12.3198	−	37.9164i	−0.455976	−	1.40335i
$731$	18.4245	+	25.3591i	0.681453	+	0.937940i
$732$		0			0
$733$	20.9894	−	6.81988i	0.775262	−	0.251898i	0.105446	−	0.994425i	$-0.466373\pi$
$733$	20.9894	−	6.81988i	0.775262	−	0.251898i	0.669816	+	0.742527i	$0.266373\pi$
$734$	1.35598	−	4.17328i	0.0500501	−	0.154038i
$735$		0			0
$736$		−	2.86730i		−	0.105690i
$737$	9.35707	−	0.675024i	0.344672	−	0.0248648i
$738$		0			0
$739$	−3.45072	+	4.74950i	−0.126937	+	0.174713i	−0.867755	−	0.496992i	$-0.834438\pi$
$739$	−3.45072	+	4.74950i	−0.126937	+	0.174713i	0.740819	+	0.671705i	$0.234438\pi$
$740$	−18.5941	−	6.04159i	−0.683533	−	0.222093i
$741$		0			0
$742$	46.3937	−	33.7070i	1.70317	−	1.23742i
$743$	1.47943	−	1.07487i	0.0542752	−	0.0394332i	−0.560317	−	0.828278i	$-0.689321\pi$
$743$	1.47943	−	1.07487i	0.0542752	−	0.0394332i	0.614592	+	0.788845i	$0.289321\pi$
$744$		0			0
$745$	−3.38098	−	1.09855i	−0.123869	−	0.0402476i
$746$	12.2045	−	16.7980i	0.446838	−	0.615020i
$747$		0			0
$748$	11.0578	+	6.87588i	0.404315	+	0.251407i
$749$			35.6531i			1.30274i
$750$		0			0
$751$	15.5034	−	47.7145i	0.565726	−	1.74113i	−0.100057	−	0.994982i	$-0.531903\pi$
$751$	15.5034	−	47.7145i	0.565726	−	1.74113i	0.665784	−	0.746145i	$-0.268097\pi$
$752$	−5.02285	+	1.63202i	−0.183164	+	0.0595137i
$753$		0			0
$754$	−8.70070	−	11.9755i	−0.316861	−	0.436121i
$755$	12.5896	+	38.7467i	0.458182	+	1.41014i
$756$		0			0
$757$	0.386810	+	0.281034i	0.0140589	+	0.0102144i	0.594792	−	0.803879i	$-0.297234\pi$
$757$	0.386810	+	0.281034i	0.0140589	+	0.0102144i	−0.580734	+	0.814094i	$0.697234\pi$
$758$	−19.5543			−0.710246
$759$		0			0
$760$	12.8796			0.467193
$761$	27.1078	+	19.6950i	0.982658	+	0.713943i	0.958301	−	0.285760i	$-0.0922461\pi$
$761$	27.1078	+	19.6950i	0.982658	+	0.713943i	0.0243573	+	0.999703i	$0.492246\pi$
$762$		0			0
$763$	2.39908	+	7.38361i	0.0868526	+	0.267305i
$764$	−6.47500	−	8.91208i	−0.234257	−	0.322428i
$765$		0			0
$766$	−25.3207	+	8.22720i	−0.914875	+	0.297261i
$767$	−7.49738	+	23.0746i	−0.270715	+	0.833175i
$768$		0			0
$769$			24.0466i			0.867144i	0.901119	+	0.433572i	$0.142747\pi$
$769$			24.0466i			0.867144i	−0.901119	+	0.433572i	$0.857253\pi$
$770$	15.0435	+	36.9991i	0.542130	+	1.33335i
$771$		0			0
$772$	11.7974	−	16.2377i	0.424597	−	0.584408i
$773$	15.8121	+	5.13766i	0.568721	+	0.184789i	0.579242	−	0.815156i	$-0.303349\pi$
$773$	15.8121	+	5.13766i	0.568721	+	0.184789i	−0.0105203	+	0.999945i	$0.503349\pi$
$774$		0			0
$775$	−10.5633	+	7.67465i	−0.379443	+	0.275682i
$776$	−8.66213	+	6.29341i	−0.310952	+	0.225920i
$777$		0			0
$778$	−20.4257	−	6.63671i	−0.732296	−	0.237937i
$779$	2.55936	−	3.52266i	0.0916986	−	0.126212i
$780$		0			0
$781$	−3.43583	−	4.07640i	−0.122944	−	0.145865i
$782$		−	11.2572i		−	0.402556i
$783$		0			0
$784$	−3.65163	+	11.2386i	−0.130415	+	0.401377i
$785$	56.7299	−	18.4327i	2.02478	−	0.657890i
$786$		0			0
$787$	18.6408	+	25.6568i	0.664471	+	0.914567i	0.999619	−	0.0275991i	$-0.00878619\pi$
$787$	18.6408	+	25.6568i	0.664471	+	0.914567i	−0.335148	+	0.942166i	$0.608786\pi$
$788$	6.30278	+	19.3980i	0.224527	+	0.691024i
$789$		0			0
$790$	−19.5448	−	14.2001i	−0.695371	−	0.505217i
$791$	62.6904			2.22901
$792$		0			0
$793$	43.4699			1.54366
$794$	−22.2046	−	16.1326i	−0.788013	−	0.572525i
$795$		0			0
$796$	1.82238	+	5.60872i	0.0645926	+	0.198796i
$797$	5.80392	+	7.98841i	0.205585	+	0.282964i	0.899342	−	0.437245i	$-0.144046\pi$
$797$	5.80392	+	7.98841i	0.205585	+	0.282964i	−0.693757	+	0.720209i	$0.744046\pi$
$798$		0			0
$799$	−19.7200	+	6.40742i	−0.697644	+	0.226678i
$800$	−0.836503	+	2.57449i	−0.0295749	+	0.0910221i
$801$		0			0
$802$		−	31.8942i		−	1.12622i
$803$	44.1218	−	17.9395i	1.55703	−	0.633072i
$804$		0			0
$805$	20.2959	−	27.9349i	0.715336	−	0.984576i
$806$	−21.4608	−	6.97302i	−0.755923	−	0.245614i
$807$		0			0
$808$	−7.17785	+	5.21501i	−0.252516	+	0.183464i
$809$	−2.89625	+	2.10425i	−0.101827	+	0.0739814i	−0.637533	−	0.770423i	$-0.720045\pi$
$809$	−2.89625	+	2.10425i	−0.101827	+	0.0739814i	0.535707	+	0.844404i	$0.320045\pi$
$810$		0			0
$811$	−12.6449	−	4.10856i	−0.444021	−	0.144271i	0.0784691	−	0.996917i	$-0.474997\pi$
$811$	−12.6449	−	4.10856i	−0.444021	−	0.144271i	−0.522490	+	0.852645i	$0.674997\pi$
$812$	8.06760	−	11.1041i	0.283117	−	0.389677i
$813$		0			0
$814$	5.60071	−	22.6759i	0.196305	−	0.794790i
$815$		−	30.2977i		−	1.06128i
$816$		0			0
$817$	−11.4462	+	35.2278i	−0.400452	+	1.23247i
$818$	−18.7363	+	6.08779i	−0.655099	+	0.212855i
$819$		0			0
$820$	1.53149	+	2.10791i	0.0534818	+	0.0736114i
$821$	4.53634	+	13.9614i	0.158319	+	0.487257i	0.998482	−	0.0550775i	$-0.0175406\pi$
$821$	4.53634	+	13.9614i	0.158319	+	0.487257i	−0.840163	+	0.542334i	$0.817541\pi$
$822$		0			0
$823$	9.99145	+	7.25921i	0.348280	+	0.253040i	0.748147	−	0.663533i	$-0.230944\pi$
$823$	9.99145	+	7.25921i	0.348280	+	0.253040i	−0.399867	+	0.916573i	$0.630944\pi$
$824$	−1.20660			−0.0420340
$825$		0			0
$826$	−22.4966			−0.782758
$827$	−22.1099	−	16.0638i	−0.768838	−	0.558593i	0.132771	−	0.991147i	$-0.457613\pi$
$827$	−22.1099	−	16.0638i	−0.768838	−	0.558593i	−0.901608	+	0.432554i	$0.857613\pi$
$828$		0			0
$829$	−13.1278	−	40.4033i	−0.455948	−	1.40326i	−0.870019	−	0.493019i	$-0.835893\pi$
$829$	−13.1278	−	40.4033i	−0.455948	−	1.40326i	0.414070	−	0.910245i	$-0.364107\pi$
$830$	−15.5535	−	21.4075i	−0.539869	−	0.743066i
$831$		0			0
$832$	−4.44929	+	1.44566i	−0.154251	+	0.0501193i
$833$	−14.3365	+	44.1233i	−0.496731	+	1.52878i
$834$		0			0
$835$			18.1293i			0.627391i
$836$	1.10716	+	15.3472i	0.0382918	+	0.530795i
$837$		0			0
$838$	−13.9259	+	19.1674i	−0.481062	+	0.662125i
$839$	11.6200	+	3.77558i	0.401168	+	0.130347i	0.502650	−	0.864490i	$-0.332358\pi$
$839$	11.6200	+	3.77558i	0.401168	+	0.130347i	−0.101482	+	0.994837i	$0.532358\pi$
$840$		0			0
$841$	15.3620	−	11.1611i	0.529723	−	0.384866i
$842$	1.40999	−	1.02442i	0.0485915	−	0.0353038i
$843$		0			0
$844$	6.33088	+	2.05703i	0.217918	+	0.0708058i
$845$	−14.5001	+	19.9577i	−0.498820	+	0.686566i
$846$		0			0
$847$	−42.7946	+	21.1062i	−1.47044	+	0.725217i
$848$			13.2199i			0.453972i
$849$		0			0
$850$	−3.28416	+	10.1076i	−0.112646	+	0.346688i
$851$	−19.2046	+	6.23996i	−0.658326	+	0.213903i
$852$		0			0
$853$	−31.5640	−	43.4441i	−1.08073	−	1.48750i	−0.858714	−	0.512456i	$-0.828736\pi$
$853$	−31.5640	−	43.4441i	−1.08073	−	1.48750i	−0.222017	−	0.975043i	$-0.571264\pi$
$854$	12.4555	+	38.3341i	0.426218	+	1.31176i
$855$		0			0
$856$	−6.64938	−	4.83105i	−0.227271	−	0.165122i
$857$	−34.0024			−1.16150			−0.580751	−	0.814081i	$-0.697241\pi$
$857$	−34.0024			−1.16150			−0.580751	+	0.814081i	$0.697241\pi$
$858$		0			0
$859$	22.0621			0.752748			0.376374	−	0.926468i	$-0.377171\pi$
$859$	22.0621			0.752748			0.376374	+	0.926468i	$0.377171\pi$
$860$	−17.9316	−	13.0281i	−0.611462	−	0.444253i
$861$		0			0
$862$	7.93234	+	24.4132i	0.270177	+	0.831518i
$863$	−22.9248	−	31.5533i	−0.780371	−	1.07409i	−0.995241	−	0.0974454i	$-0.968933\pi$
$863$	−22.9248	−	31.5533i	−0.780371	−	1.07409i	0.214870	−	0.976643i	$-0.431067\pi$
$864$		0			0
$865$	−18.8812	+	6.13486i	−0.641979	+	0.208591i
$866$	0.740579	−	2.27927i	0.0251659	−	0.0774526i
$867$		0			0
$868$		−	20.9232i		−	0.710181i
$869$	15.2406	−	24.5100i	0.517002	−	0.831445i
$870$		0			0
$871$	−7.77810	+	10.7056i	−0.263551	+	0.362747i
$872$	−1.70214	−	0.553058i	−0.0576416	−	0.0187289i
$873$		0			0
$874$	10.7620	−	7.81902i	0.364029	−	0.264482i
$875$	22.3399	−	16.2309i	0.755227	−	0.548705i
$876$		0			0
$877$	26.1960	+	8.51161i	0.884577	+	0.287417i	0.715857	−	0.698247i	$-0.246036\pi$
$877$	26.1960	+	8.51161i	0.884577	+	0.287417i	0.168721	+	0.985664i	$0.446036\pi$
$878$	8.35336	−	11.4974i	0.281912	−	0.388019i
$879$		0			0
$880$	−8.93882	−	2.20780i	−0.301327	−	0.0744248i
$881$		−	27.6311i		−	0.930914i	−0.885071	−	0.465457i	$-0.845890\pi$
$881$		−	27.6311i		−	0.930914i	0.885071	−	0.465457i	$-0.154110\pi$
$882$		0			0
$883$	−12.8141	+	39.4376i	−0.431227	+	1.32718i	0.465676	+	0.884955i	$0.345811\pi$
$883$	−12.8141	+	39.4376i	−0.431227	+	1.32718i	−0.896903	+	0.442226i	$0.854189\pi$
$884$	−17.4682	+	5.67576i	−0.587518	+	0.190896i
$885$		0			0
$886$	10.9319	+	15.0465i	0.367264	+	0.505496i
$887$	14.4120	+	44.3555i	0.483907	+	1.48931i	0.833558	+	0.552433i	$0.186300\pi$
$887$	14.4120	+	44.3555i	0.483907	+	1.48931i	−0.349650	+	0.936880i	$0.613700\pi$
$888$		0			0
$889$	42.0475	+	30.5493i	1.41023	+	1.02459i
$890$	19.5813			0.656368
$891$		0			0
$892$	21.8044			0.730067
$893$	−19.8227	−	14.4020i	−0.663340	−	0.481945i
$894$		0			0
$895$	−18.1138	−	55.7486i	−0.605478	−	1.86347i
$896$	−2.54972	−	3.50939i	−0.0851803	−	0.117241i
$897$		0			0
$898$	26.6686	−	8.66515i	0.889942	−	0.289160i
$899$	−4.71616	+	14.5148i	−0.157293	+	0.484097i
$900$		0			0
$901$			51.9021i			1.72911i
$902$	−2.38012	+	2.00610i	−0.0792492	+	0.0667960i
$903$		0			0
$904$	−8.49465	+	11.6919i	−0.282528	+	0.388866i
$905$	−12.7384	−	4.13894i	−0.423437	−	0.137583i
$906$		0			0
$907$	15.6504	−	11.3707i	0.519662	−	0.377556i	−0.296815	−	0.954935i	$-0.595924\pi$
$907$	15.6504	−	11.3707i	0.519662	−	0.377556i	0.816476	+	0.577379i	$0.195924\pi$
$908$	1.97875	−	1.43765i	0.0656672	−	0.0477100i
$909$		0			0
$910$	−53.5805	−	17.4094i	−1.77618	−	0.577115i
$911$	−7.76256	+	10.6842i	−0.257185	+	0.353985i	−0.918011	−	0.396554i	$-0.870206\pi$
$911$	−7.76256	+	10.6842i	−0.257185	+	0.353985i	0.660826	+	0.750539i	$0.270206\pi$
$912$		0			0
$913$	24.1720	−	20.3736i	0.799976	−	0.674268i
$914$		−	13.3451i		−	0.441416i
$915$		0			0
$916$	2.19324	−	6.75009i	0.0724666	−	0.223029i
$917$	−16.6457	+	5.40850i	−0.549688	+	0.178605i
$918$		0			0
$919$	−11.1523	−	15.3498i	−0.367879	−	0.506343i	0.584444	−	0.811434i	$-0.301313\pi$
$919$	−11.1523	−	15.3498i	−0.367879	−	0.506343i	−0.952323	+	0.305092i	$0.901313\pi$
$920$	2.45979	+	7.57045i	0.0810968	+	0.249590i
$921$		0			0
$922$	−7.87231	−	5.71957i	−0.259261	−	0.188364i
$923$	7.51995			0.247522
$924$		0			0
$925$	19.0639			0.626817
$926$	−5.68437	−	4.12993i	−0.186800	−	0.135718i
$927$		0			0
$928$	0.977763	+	3.00925i	0.0320966	+	0.0987833i
$929$	16.8849	+	23.2400i	0.553975	+	0.762481i	0.990545	−	0.137189i	$-0.0438069\pi$
$929$	16.8849	+	23.2400i	0.553975	+	0.762481i	−0.436570	+	0.899670i	$0.643807\pi$
$930$		0			0
$931$	−52.1400	+	16.9413i	−1.70882	+	0.555230i
$932$	−5.32502	+	16.3887i	−0.174427	+	0.536830i
$933$		0			0
$934$			9.52380i			0.311628i
$935$	−35.0943	−	8.66794i	−1.14771	−	0.283472i
$936$		0			0
$937$	−16.9818	+	23.3734i	−0.554770	+	0.763576i	−0.990650	−	0.136429i	$-0.956437\pi$
$937$	−16.9818	+	23.3734i	−0.554770	+	0.763576i	0.435880	+	0.900005i	$0.356437\pi$
$938$	−11.6695	−	3.79164i	−0.381022	−	0.123801i
$939$		0			0
$940$	11.8616	−	8.61796i	0.386883	−	0.281087i
$941$	14.1509	−	10.2812i	0.461305	−	0.335158i	−0.332738	−	0.943019i	$-0.607972\pi$
$941$	14.1509	−	10.2812i	0.461305	−	0.335158i	0.794043	+	0.607861i	$0.207972\pi$
$942$		0			0
$943$	2.55936	+	0.831587i	0.0833442	+	0.0270802i
$944$	3.04833	−	4.19567i	0.0992147	−	0.136557i
$945$		0			0
$946$	13.9827	−	22.4870i	0.454616	−	0.731116i
$947$		−	50.9283i		−	1.65495i	−0.561505	−	0.827473i	$-0.689777\pi$
$947$		−	50.9283i		−	1.65495i	0.561505	−	0.827473i	$-0.310223\pi$
$948$		0			0
$949$	−20.7609	+	63.8954i	−0.673926	+	2.07413i
$950$	−11.9441	+	3.88086i	−0.387517	+	0.125912i
$951$		0			0
$952$	−10.0104	−	13.7781i	−0.324438	−	0.446551i
$953$	−7.92640	−	24.3950i	−0.256761	−	0.790230i	−0.993478	−	0.114028i	$-0.963625\pi$
$953$	−7.92640	−	24.3950i	−0.256761	−	0.790230i	0.736716	−	0.676202i	$-0.236375\pi$
$954$		0			0
$955$	24.7412	+	17.9755i	0.800607	+	0.581675i
$956$	19.4100			0.627764
$957$		0			0
$958$	8.52670			0.275485
$959$	−38.8279	−	28.2101i	−1.25382	−	0.910951i
$960$		0			0
$961$	−2.39014	−	7.35610i	−0.0771014	−	0.237294i
$962$	19.3655	+	26.6544i	0.624370	+	0.859371i
$963$		0			0
$964$	−12.8473	+	4.17435i	−0.413784	+	0.134447i
$965$	−17.2184	+	52.9926i	−0.554278	+	1.70589i
$966$		0			0
$967$		−	13.5640i		−	0.436190i	−0.975928	−	0.218095i	$-0.930016\pi$
$967$		−	13.5640i		−	0.436190i	0.975928	−	0.218095i	$-0.0699843\pi$
$968$	1.86239	−	10.8412i	0.0598595	−	0.348449i
$969$		0			0
$970$	17.4714	−	24.0473i	0.560973	−	0.772113i
$971$	31.7512	+	10.3166i	1.01894	+	0.331075i	0.770410	−	0.637549i	$-0.220051\pi$
$971$	31.7512	+	10.3166i	1.01894	+	0.331075i	0.248533	+	0.968623i	$0.420051\pi$
$972$		0			0
$973$	−12.3153	+	8.94761i	−0.394811	+	0.286847i
$974$	−12.7393	+	9.25567i	−0.408195	+	0.296571i
$975$		0			0
$976$	−8.83711	−	2.87135i	−0.282869	−	0.0919098i
$977$	−14.1713	+	19.5052i	−0.453381	+	0.624026i	−0.973120	−	0.230300i	$-0.926029\pi$
$977$	−14.1713	+	19.5052i	−0.453381	+	0.624026i	0.519739	+	0.854325i	$0.326029\pi$
$978$		0			0
$979$	1.68325	+	23.3329i	0.0537969	+	0.745723i
$980$		−	32.8055i		−	1.04793i
$981$		0			0
$982$	−12.8057	+	39.4118i	−0.408645	+	1.25768i
$983$	50.0891	−	16.2749i	1.59759	−	0.519090i	0.631083	−	0.775715i	$-0.282611\pi$
$983$	50.0891	−	16.2749i	1.59759	−	0.519090i	0.966511	+	0.256625i	$0.0826107\pi$
$984$		0			0
$985$	−33.2821	−	45.8089i	−1.06046	−	1.45959i
$986$	3.83876	+	11.8145i	0.122251	+	0.376250i
$987$		0			0
$988$	−17.5591	−	12.7574i	−0.558630	−	0.405868i
$989$	−22.8924			−0.727937
$990$		0			0
$991$	−31.1710			−0.990178			−0.495089	−	0.868842i	$-0.664865\pi$
$991$	−31.1710			−0.990178			−0.495089	+	0.868842i	$0.664865\pi$
$992$	3.90222	+	2.83513i	0.123896	+	0.0900155i
$993$		0			0
$994$	2.15470	+	6.63150i	0.0683431	+	0.210338i
$995$	−9.62317	−	13.2452i	−0.305075	−	0.419900i
$996$		0			0
$997$	−21.8526	+	7.10034i	−0.692079	+	0.224870i	−0.633876	−	0.773435i	$-0.718537\pi$
$997$	−21.8526	+	7.10034i	−0.692079	+	0.224870i	−0.0582029	+	0.998305i	$0.518537\pi$
$998$	8.39596	−	25.8401i	0.265769	−	0.817954i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.l.a.161.1	yes	8
3.2	odd	2		198.2.l.b.161.2	yes	8
4.3	odd	2		1584.2.cd.a.161.1		8
11.5	even	5		2178.2.b.j.2177.7		8
11.6	odd	10		2178.2.b.i.2177.7		8
11.8	odd	10		198.2.l.b.107.2	yes	8
12.11	even	2		1584.2.cd.b.161.2		8
33.5	odd	10		2178.2.b.i.2177.2		8
33.8	even	10	inner	198.2.l.a.107.1	✓	8
33.17	even	10		2178.2.b.j.2177.2		8
44.19	even	10		1584.2.cd.b.305.2		8
132.107	odd	10		1584.2.cd.a.305.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.l.a.107.1	✓	8	33.8	even	10	inner
198.2.l.a.161.1	yes	8	1.1	even	1	trivial
198.2.l.b.107.2	yes	8	11.8	odd	10
198.2.l.b.161.2	yes	8	3.2	odd	2
1584.2.cd.a.161.1		8	4.3	odd	2
1584.2.cd.a.305.1		8	132.107	odd	10
1584.2.cd.b.161.2		8	12.11	even	2
1584.2.cd.b.305.2		8	44.19	even	10
2178.2.b.i.2177.2		8	33.5	odd	10
2178.2.b.i.2177.7		8	11.6	odd	10
2178.2.b.j.2177.2		8	33.17	even	10
2178.2.b.j.2177.7		8	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.63178 - 2.24595i) q^{5} +(-4.12554 + 1.34047i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.63178 - 2.24595i) q^{5} +(-4.12554 + 1.34047i) q^{7} +(0.309017 - 0.951057i) q^{8} +2.77615i q^{10} +(-3.30803 + 0.238643i) q^{11} +(2.74981 - 3.78479i) q^{13} +(4.12554 + 1.34047i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-3.17625 + 2.30768i) q^{17} +(-4.41232 - 1.43365i) q^{19} +(1.63178 - 2.24595i) q^{20} +(2.81652 + 1.75134i) q^{22} -2.86730i q^{23} +(-0.836503 + 2.57449i) q^{25} +(-4.44929 + 1.44566i) q^{26} +(-2.54972 - 3.50939i) q^{28} +(0.977763 + 3.00925i) q^{29} +(3.90222 + 2.83513i) q^{31} +1.00000 q^{32} +3.92606 q^{34} +(9.74258 + 7.07840i) q^{35} +(-2.17625 - 6.69781i) q^{37} +(2.72696 + 3.75334i) q^{38} +(-2.64027 + 0.857876i) q^{40} +(-0.290024 + 0.892603i) q^{41} -7.98397i q^{43} +(-1.24920 - 3.07238i) q^{44} +(-1.68536 + 2.31969i) q^{46} +(5.02285 + 1.63202i) q^{47} +(9.56009 - 6.94582i) q^{49} +(2.18999 - 1.59112i) q^{50} +(4.44929 + 1.44566i) q^{52} +(7.77045 - 10.6951i) q^{53} +(5.93394 + 7.04025i) q^{55} +4.33785i q^{56} +(0.977763 - 3.00925i) q^{58} +(-4.93230 + 1.60260i) q^{59} +(5.46164 + 7.51730i) q^{61} +(-1.49052 - 4.58734i) q^{62} +(-0.809017 - 0.587785i) q^{64} -12.9875 q^{65} -2.82859 q^{67} +(-3.17625 - 2.30768i) q^{68} +(-3.72134 - 11.4531i) q^{70} +(0.944821 + 1.30043i) q^{71} +(-13.6579 + 4.43773i) q^{73} +(-2.17625 + 6.69781i) q^{74} -4.63939i q^{76} +(13.3275 - 5.41884i) q^{77} +(-5.11504 + 7.04025i) q^{79} +(2.64027 + 0.857876i) q^{80} +(0.759294 - 0.551659i) q^{82} +(-7.71124 + 5.60255i) q^{83} +(10.3659 + 3.36807i) q^{85} +(-4.69286 + 6.45917i) q^{86} +(-0.795274 + 3.21987i) q^{88} -7.05342i q^{89} +(-6.27106 + 19.3003i) q^{91} +(2.72696 - 0.886044i) q^{92} +(-3.10429 - 4.27269i) q^{94} +(3.98002 + 12.2492i) q^{95} +(-8.66213 - 6.29341i) q^{97} -11.8169 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8	\( 8 q - 2 q^{2} - 2 q^{4} - 2 q^{8} + 4 q^{11} - 2 q^{16} - 8 q^{17} - 6 q^{22} + 6 q^{25} - 20 q^{26} - 10 q^{28} + 10 q^{29} - 14 q^{31} + 8 q^{32} - 8 q^{34} + 10 q^{35} + 20 q^{38} - 10 q^{40} - 8 q^{41} - 6 q^{44} + 20 q^{46} + 20 q^{47} + 6 q^{49} - 4 q^{50} + 20 q^{52} + 30 q^{53} + 28 q^{55} + 10 q^{58} - 20 q^{59} + 20 q^{61} + 16 q^{62} - 2 q^{64} - 64 q^{65} - 56 q^{67} - 8 q^{68} + 10 q^{70} + 20 q^{71} - 10 q^{73} - 20 q^{79} + 10 q^{80} + 12 q^{82} - 12 q^{83} + 20 q^{86} - 6 q^{88} + 20 q^{92} - 20 q^{94} + 16 q^{95} - 12 q^{97} - 44 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 - 2 * q^4 - 2 * q^8 + 4 * q^11 - 2 * q^16 - 8 * q^17 - 6 * q^22 + 6 * q^25 - 20 * q^26 - 10 * q^28 + 10 * q^29 - 14 * q^31 + 8 * q^32 - 8 * q^34 + 10 * q^35 + 20 * q^38 - 10 * q^40 - 8 * q^41 - 6 * q^44 + 20 * q^46 + 20 * q^47 + 6 * q^49 - 4 * q^50 + 20 * q^52 + 30 * q^53 + 28 * q^55 + 10 * q^58 - 20 * q^59 + 20 * q^61 + 16 * q^62 - 2 * q^64 - 64 * q^65 - 56 * q^67 - 8 * q^68 + 10 * q^70 + 20 * q^71 - 10 * q^73 - 20 * q^79 + 10 * q^80 + 12 * q^82 - 12 * q^83 + 20 * q^86 - 6 * q^88 + 20 * q^92 - 20 * q^94 + 16 * q^95 - 12 * q^97 - 44 * q^98

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